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Alex787 [66]
2 years ago
13

If the log↓b(a)=0, what is the value of a?explain why log↓0 (3) and log↓1 (3) do not exist. ​

Mathematics
1 answer:
Sloan [31]2 years ago
5 0

Answer:

1. a = 1

2. See explanation below.

Step-by-step explanation:

<u>First Question</u>

Given:

\displaystyle \large{\log_b a = 0}

Convert to exponential:

\displaystyle \large{\log_b a = c \to b^c = a}

Thus \displaystyle \large{\log_b a = 0 \to b^0 = a}

Evaluate:

\displaystyle \large{b^0 = a}

We know that for every values to power of 0 will always result in 1, excluding 0 to power of 0 itself.

Solution:

\displaystyle \large{a = 1}

__________________________________________________________

<u>Second Question</u>

Given:

\displaystyle \large{log_0 3} and \displaystyle \large{\log_1 3}

Let’s convert to an equation:

\displaystyle \large{\log_0 3 = x} and \displaystyle \large{\log_1 3 = y}

The variables represent unknown values of logarithm.

Convert to exponential:

\displaystyle \large{0^x = 3} and \displaystyle \large{1^y = 3}

Notice that none of x-values and y-values will satisfy the equations. No matter what real numbers you put in, these equations will always be false.

Hence, no solutions for x and y.

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Use a inequality symbol to compare -3x+7 -10-2
abruzzese [7]
Hey there,

Let's remember that a (inequality symbol) is things like (<), (>), (≤),(≥), (≠).

So, I believe that (-3x+7) and (-10-2) are separate. So we will find that out :)

Let's first do (-3x+7). As simplifying this expression here, we take that "x" of for a while and just stick to (-3+7). 

    -3
+   7
______
     4

Let's bring that "x" back, and the answer would be 4x for a while.

So far, 4x is the answer.
_____________________________________________________________

Now, Let's work on the other side.

We are talking about (<span>-10-2)

    -10
-      2
_______
</span>     -12

So, by solving the answer to (-10-2), we got -12.

So, let's determine what is greater . . . . . 

What \ is \ greater?

-12 or 4.

-12 is on the negative side, and the number 4 is positive. This would conclude that 4 is great than -12.

Your correct answer would look like . . . 

<span>(-3x+7) > (-10-2)
</span>
I really hope this helps you alot.

~Jurgen

8 0
3 years ago
Read 2 more answers
If x = 1 is a common root of ax² +ax + 2 = 0 and x² + x + b = 0 , then ab =
vodka [1.7K]

Answer:

ab = 2

Step-by-step explanation:

Given equations

ax² +ax + 2 = 0

x² + x + b = 0

root of both the equation

x= 1

then we can plug in x = 1 in both the equation

ax² +ax + 2 = 0                        x² + x + b = 0

a*1² +a*1 + 2 = 0                        1² + 1 + b = 0

a +a + 2 = 0                                 1 + 1 + b = 0

2a + 2 = 0                                    2 + b = 0

2a = -  2                                         b = -2

a = -2/2 = -1

Thus,

a = -1

b = -2

a*b = -1*-2 = 2

ab = 2

6 0
3 years ago
Pleaseeeeeee help mee
BlackZzzverrR [31]

Answer:

The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

Step-by-step explanation:

<u><em>Step(i):</em></u>-

Given  

                cos( 3x - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

                  cos( 3x - \frac{\pi }{3} )  = cos (\frac{\pi }{6} )

                      3x - \frac{\pi }{3}  =  \frac{\pi }{6}

                      3x - \frac{\pi }{3  } + \frac{\pi }{3}   =  \frac{\pi }{6} + \frac{\pi }{3}

                      3x = \frac{2\pi +\pi }{6} = \frac{3\pi }{6} = \frac{\pi }{2}

                     x = \frac{\pi }{6}

<u><em>Step(ii)</em></u>:-

The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

<u><em>verification </em></u>:-

      cos( 3x - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

put  x = \frac{\pi }{6}

    cos( 3(\frac{\pi }{6})  - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

    cos (\frac{\pi }{6} ) = \frac{\sqrt{3} }{2} \\\\\frac{\sqrt{3} }{2} =  \frac{\sqrt{3} }{2}

Both are equal

∴The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

                     

4 0
2 years ago
The following numerically ordered sequence of numbers has a mean
Vladimir79 [104]
Median =  middle number

Total ten numbers so 
median =   (17 + b)/2
given median = 18
so
(17 + b)/  2 = 18
17+b = 36
b = 36 - 17
b = 19

Now you have the data set
7, a , 12, 15 , 17, 19, 20, 22, 24 , 25

Mean =  (7 + a + 12+ 15 +17 + 19 + 20 + 22 +24  +25)/ 10
Given mean = 17

so
17 = (7 + a + 12+ 15 +17 + 19 + 20 + 22 +24  +25)/ 10
17 = (a + 161) / 10
a + 161 = 170
a = 170 - 161
a = 9

answer
a = 9
b = 19
7 0
3 years ago
Read 2 more answers
Sinmplify the expression -3(-5y+2)-(8y-3)<br> a) 7y-3<br> b)7y-9<br> c)23y-3
raketka [301]

Answer:

a) 7y - 3

Step-by-step explanation:

- 3( - 5y + 2) - (8y - 3)

15y - 6 - (8y - 3)

15y - 6 - 8y  + 3

7y - 6 + 3

\boxed{\green{ = 7y - 3}}

8 0
3 years ago
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