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

Answer:

0.08

Step-by-step 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.