algebra question wk3

Question

Solve the following exponential equation:

5^x = 2

Round your solution to the nearest hundredth.

Answer 1

ln 5^x = ln 2

x ln 5 = ln 2

x = ln 2 / ln 5

Can you use your calculator to determine x and answer?

Answer 2

Take the logarithm of both sides. To make it easy, use log base 5 (log₅):

log₅(5^x) = log₅(2)

One of the properties of logarithms is that when there is an exponent inside the logarithm, you can move it out front as a multiplier:

(x)log₅(5) = log₅(2)

Another rule of logarithms is the log_b(b) = 1 so since log₅(5) = 1 then:

x = log₅(2)

To get the value, plug this into a calculator.