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3 years ago

Solve 4x − 5 = 6 for x using the change of base formula log base b of y equals log y over log b.

Mathematics

2 answers:

den301095 [7]3 years ago

6 0

Answer:

Step-by-step explanation:

4^x-5 = 6

<u>Apply the ln rule</u>

x^y = z

(y)*ln(x) = z

4^x-5 = 6

(x-5)*ln(4) = ln(6)

x-5 = ln(6)/ln(4)

x-5 = 1.292

x = 6.292

Therefore, the correct answer is the last option.

AlexFokin [52]3 years ago

4 0

Answer:

Option 4 - x=6.292

Step-by-step explanation:

Given : Expression $4^{x-5}=6$

To find : Solve the expression using change of base formula?

Solution :

Expression $4^{x-5}=6$

Change of base formula is $\log_b y=\frac{\log_a y}{\log_a b}$

Step 1 - Taking log both side in the expression,

$\log(4^{x-5})=\log (6)$

Apply logarithmic property, $\log a^x=x\log a$

$(x-5)\log(4)=\log (6)$

Step 2 - Taking log one side,

$x-5=\frac{\log (6)}{\log(4)}$

Step 3 - Apply change base formula,

$x-5=\log_4 6$

Step 4 - Solve,

$x=\log_4 6+5$

$x=1.292+5$

$x=6.292$

Therefore, Option 4 is correct.

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For how many three digit numbers (100 to 999) is the sum of the digits even? (For example, 343 has an even sum of digits: 3 + 4

n200080 [17]

Answer:

there are 425 numbers of three digits whose the sum of the digits is even.

Step-by-step explanation:

Option 1:

It is necessary to accomplish one of the next conditions:

(1) all of the digits are even.

(2) exactly 2 of the digits are odd

Then, for the first condition:

4x5x5 = 100 -> this is because the first digit can not be 0.

for the second condition:

(3C1)*5*5*5-1*5*5 =3*125-25=350

where 3C1 is a combination. The 3C1 determines which of the three digits is even, and it is necessary to subtract the numbers under 100 with the other 2 digits odd.

So, there are 450 numbers of three digits whose the sum of the digits is even.

Option 2:

there are 900 three digit number and 5*5*5 =125 has 3 odd numbers and 5*5*5+4*5*5+4*5*5=325 has 1 odd number, so there are 450 numbers of three digits whose the sum of the digitis is odd, so 900-450 whose the sum of the digits is even.

4 0

3 years ago

Six more years than 2/3 George age is 16 .How old is George

Mashutka [201]

Answer:21

Step-by-step explanation:i did the math

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3 years ago

Given that R=9x+8y find x when y=8 and R=4

Ilya [14]

Answer:

Step-by-step explanation:

R = 9x + 8y

4 = 9x + 8*8

4 = 9x + 64

Subtract 64 from both sides

4 - 64 = 9x + 64 - 64

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Divide both sides by 9

-60/9 = 9x/9

-20/3 = x

x = -6 2/3

8 0

4 years ago

Read 2 more answers

What is the quotient 2y^-6y-20/4y+12 ÷ y+5y+6/3y^2+28y+27

malfutka [58]

Answer with explanation:

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