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larisa86 [58]
3 years ago
14

BRAINLIEST FOR THE CORRECT PROOF: prove, a^logx base a=x

Mathematics
1 answer:
givi [52]3 years ago
7 0
a^{\log_a x}=x \Leftrightarrow \log_ax=\log_ax
You might be interested in
Fill in the missing expression
padilas [110]

Answer:

The complete table is:

[ 5a ]           +    [ a + 3 ]      +    [ 4a ]     =    [ 10a + 3 ]

  +                         +                    +                    +

[ 2b ]          +     [ 4 + a ]      +     [ -a  ]     =    [  2b + 4 ]

  +                       +                     +                    +

[ 2a ]          +    [ a + 1 ]       +   [  -3a  ]    =   [     1      ]

  =                      =                     =                     =

[ 7a + 2b ]  +   [ 3a + 8 ]    +     [   0   ]    =   [10a + 2b + 8 ]

Explanation:

You can determine the content of each box by subtraction, running the rows and the columns.

The expressions are:

[ 5a ]  +    [          ]   +    [ 4a ]     =    [ 10a + 3 ]

  +                +                +                    +

[ 2b ]  +   [ 4 + a ]   +     [      ]     =    [              ]

  +              +                   +                    +

[      ]   +   [         ]   +      [  -3a  ]  =   [     1      ]

  =               =                   =                   =

[      ]  +   [ 3a + 8 ]  +  [         ]    =   [10a + 2b + 8 ]

<u>1. First row:</u>

[ 5a ]  +    [          ]   +    [ 4a ]     =    [ 10a + 3 ]

[      ] = [10a+ 3]  - [ 4a ] - [ 5a ] = 10a - 4a - 5a + 3 = a + 3

<u>2. Second colum:</u>

[ a + 3 ] + [ 4 + a ] + [       ] =  [ 3a + 8 ]

[        ] = [ 3a + 8 ] - [ a + 3 ] - [ 4 + a ] = 3a - a  + a  + 8 - 4 - 3 = a + 1

So far, you have completed this:

[ 5a ]  +    [ a + 3 ]   +    [ 4a ]     =    [ 10a + 3 ]

  +                +                +                    +

[ 2b ]  +   [ 4 + a ]   +     [      ]     =    [              ]

  +              +                   +                    +

[      ]   +   [ a + 1 ]   +     [  -3a  ]  =   [     1      ]

  =               =                   =                   =

[      ]  +   [ 3a + 8 ]  +  [         ]    =   [10a + 2b + 8 ]

<u></u>

<u>3. Complete the row 3:</u>

<u></u>

     [      ]   +   [ a + 1 ]   +      [  -3a  ]  =   [     1      ]

    [      ]   =    [     1      ]   -   [ a + 1 ]   -    [  -3a  ]  = - a + 3a + 1 - 1 = 2a

So far, you have completed this:

[ 5a ]  +    [ a + 3 ]   +    [ 4a ]     =    [ 10a + 3 ]

  +                +                +                    +

[ 2b ]  +   [ 4 + a ]   +     [      ]     =    [              ]

  +              +                   +                    +

[   2a   ]   +   [ a + 1 ]   +     [  -3a  ]  =   [     1      ]

  =               =                   =                   =

[      ]  +   [ 3a + 8 ]  +  [         ]    =   [10a + 2b + 8 ]

<u></u>

<u>4. Complete the fourth column:</u>

[ 10a + 3 ] + [    ] + [   1   ] = [10a + 2b + 8 ]

[    ] = 10a + 2b + 8 - 10a - 3 - 1 = 2b + 4

So far, this is the results:

[ 5a ]  +    [ a + 3 ]   +    [ 4a ]     =    [ 10a + 3 ]

  +                +                +                    +

[ 2b ]  +   [ 4 + a ]   +     [      ]     =    [  2b + 4 ]

  +              +                   +                    +

[   2a   ]   +   [ a + 1 ]   +     [  -3a  ]  =   [     1      ]

  =               =                   =                   =

[      ]  +   [ 3a + 8 ]  +  [         ]    =   [10a + 2b + 8 ]

<u>5. Complete the second row:</u>

[ 2b ]  +   [ 4 + a ]   +     [      ]     =    [  2b + 4 ]

 [      ]   =   [  2b + 4 ] - [ 2b ]  -   [ 4 + a ]  = 2b - 2b + 4 - 4 - a = - a

So far:

[ 5a ]  +    [ a + 3 ]      +    [ 4a ]     =    [ 10a + 3 ]

  +                +                    +                    +

[ 2b ]  +   [ 4 + a ]      +     [ -a  ]     =    [  2b + 4 ]

  +               +                     +                    +

[   2a   ]   +   [ a + 1 ]   +   [  -3a  ]  =   [     1      ]

  =               =                    =                   =

[      ]  +   [ 3a + 8 ]  +     [         ]    =   [10a + 2b + 8 ]

<u>6. Complete the first colum:</u>

[ 5a ] + [ 2b ] + [2a ] = [   ]

[   ] = [ 7a + 2b ]

So far:

[ 5a ]           +    [ a + 3 ]      +    [ 4a ]     =    [ 10a + 3 ]

  +                         +                    +                    +

[ 2b ]           +   [ 4 + a ]      +     [ -a  ]     =    [  2b + 4 ]

  +                       +                     +                    +

[ 2a ]          +   [ a + 1 ]       +   [  -3a  ]    =   [     1      ]

  =                      =                     =                    =

[ 7a + 2b ]  +   [ 3a + 8 ]   +     [         ]    =   [10a + 2b + 8 ]

<u>7. Complete the last row:</u>

[ 7a + 2b ]  +   [ 3a + 8 ]   +     [         ]    =   [10a + 2b + 8 ]

[         ]    =   [10a + 2b + 8 ] - [ 7a + 2b ] - [ 3a + 8 ] = 0

The complete table is:

[ 5a ]           +    [ a + 3 ]      +    [ 4a ]     =    [ 10a + 3 ]

  +                         +                    +                    +

[ 2b ]           +   [ 4 + a ]      +     [ -a  ]     =    [  2b + 4 ]

  +                       +                     +                    +

[ 2a ]          +   [ a + 1 ]       +     [ -3a  ]    =   [     1      ]

  =                      =                     =                     =

[ 7a + 2b ]  +   [ 3a + 8 ]    +     [   0  ]     =   [10a + 2b + 8 ]

5 0
3 years ago
For a particular​ event, 771 tickets were sold for a total of ​$3037. If students paid ​$3 per ticket and non-students paid ​$5
BlackZzzverrR [31]

Answer:

Number of student tickets were sold = 409

Step-by-step explanation:

Total number of tickets sold = 771

I.e Students ticket (S) + Non students ticket(N S)  = 771

Total amount to be paid for tickets = $ 3037

Amount paid by students per tickets = $3

Amount paid by non-students per tickets = $5

So, according to question

S + NS = 771

3 S + 5 NS = 3037

Solve both equations  

5 S + 5 NS = 771 × 5

3 S + 5 NS = 3037

so ,

(5 S + 5 NS) - (3 S + 5 NS ) = 3855 - 3037

Or, 2 S = 818

I.e S = \frac{818}{2} = 409

Hence, The number of student tickets were sold = 409      Answer

5 0
2 years ago
Find the limit of the function by using direct substitution.
musickatia [10]
Lim x->1 (x^2+8x-2)

substitute x =1
= 1^2 +8(1)-2
= 1 +8 -2
= 7

So the limit = 7
5 0
3 years ago
The density of ethanol is around 0.8g/mL. What is the mass of 20mL of ethanol?
Harman [31]

Answer: 0.7893g//mL

If 20 mL of ethanol (density =0.7893g//mL) is mixed with 40mL water (density = 0.9971g//mL)

Step-by-step explanation:

4 0
3 years ago
It describes itself &lt;3
irina [24]

Answer:

432 ft²

Step-by-step explanation:

The formula of finding the area of a trapezoid: (base 1 + base 2/ 2) x h

(base 1 + base 2/ 2) x h

= (20 + 28/2) x 18

= 24 x 18

= 432 ft²

3 0
3 years ago
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