Question

Solve each exponential equation by using properties of common logarithms. When necessary, round answers to the nearest hundredth. 7 ^3x-1 = 5 ^x-1

x ≈ 12.33
x ≈ -3.09
x ≈ 0.08
plss help mee

Answer 1

0.08

Explanation:

Please use parentheses to indicate which operations must be done first. I 'm choosing to believe that you meant 7^(3x-1) and 5^(x-1).

Taking the common log of both sides, we get:

(3x-1)log 7 = (x-1)log 5

Then 3x·log 7 - log 7 = x log 5 - log 5

Grouping the x terms:

x(3·log 7 - log 5) = log 7 - log 5. We combine log 7 and log 5, obtaining log (7/5).

Then x(3·log 7 - log 5) = log (7/5).

Solving for x:

log (7/5)

x = ---------------------

3·log 7 - log 5

0.1461

x = ------------- = 0.08

1.0363

This agrees with the 3rd answer choice.

Answer 2

It would be the first answer; x=12.33

Explanation:

Using logaritmic properties:

question: 7^3x-1=5^x-1

log7(3x-1)=log5(x-1)

log7= 0.85 log5=0.70 (plug into calculator and substitute)

0.85(3x-1)=0.70(x-1) (distribute)

2.55x-0.85=0.7x-0.7 (solve for x)

1.85x-0.85=-0.7

1.85x=0.15

x=12.33 (final answer)