Question

Solve 5^x=81.2 round to the nearest ten-thousands

Answer 1

Answer:

x = 2.7320

Step-by-step explanation:

To solve 5^x=81.2 for x, take the log of both sides:

log 5^x = log 81.2

There is a rule of logs that allows us to rewrite log 5^x as x log 5.

Thus,

x log 5 = log 81.2, and

x = log 81.2 / log 5

which comes out to:

x = 1.90955603 / 0.698970004  = 2.73 = 2.73195704, which, when rounded to the nearest ten thousandths, yields:

x = 2.7320