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
