Solve the exponential equation. Express the solution set in terms of natural logarithms.

Question

Solve the exponential equation. Express the solution set in terms of natural logarithms.

8^5x =4

Answer 1

And just for fun, we compare the two answers...

ln 4 / (5 ln 8) =

ln 2^2 / ( 5 ln 2^3) = <--- 4 = 2^2 and 8 = 2^3

2 ln 2 / 3 (5 ln 2) <--- exponent goes in front

2 / (3*5) <--- ln 2 cancels

2/15

Answer 2

8^5x = 4

ln 8^5x = ln 4

5x ln 8 = ln 4

x = ln 4 / (5 ln 8)

Answer 3

8^5x = 4; (2³)^5x = 2², 2^15x = 2², from here 15x = 2 and x = 2/15

Answer: x = 2/15