Question

What is the solution of the equation 14^x=5?
Round your answer to the nearest ten-thousandth.

Answer 1

Take ln to both sides
ln 14^x = ln 5
then you'll get
x ln 14 = ln 5
divide both sides by ln 14
x = 0.6098533345
after rounding
x = 0.6099

Answer 2

x = 0.6099

Explanation:

To solve the question, take the logarithm of both sides to base 10. then apply the law of logarithms that states that

log aˣ = x log a

As such, 14^x=5

log 14^x= log 5

x log 14 = log 5

x = log 5 / log 14

x = 0.60985

To the nearest nearest ten-thousandth, it becomes

x = 0.6099