Question

Evaluate the logarithmic expression shown below. Round your answer to the nearest hundredth.

Answer 1

log₃ 18 = 2.63

Step-by-step explanation

To find the value of this logarithm expression, we can apply the change of base rule and then use a calculator - since calculators only have bases 10 and e,

`\log_bx=(\log_cx)/(\log_cb)`

In this case, b = 3, x = 18, and we will use the new base 10,

`\log_318=(\log_(10)18)/(\log_(10)3)\approx(1.26)/(0.48)\approx2.63`

Hence, the value is 2.63, rounded to the nearest hundredth.