Question

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

Answer 1

ln(5^x) = ln(81.2)
xln(5) = ln(81.2)
x= ln(81.2)/ln(5)
x= ln(406/5)/ln(5)
x = ln(406) - ln(5)/ln(5)
log (ab) = log(A) + log (B)
ln(2) +ln7 + ln(29 - ln(5)/ln(5)
x = 2.7320 (4dp)

Answer 2

The value of x is 2.7320 ( approx )

Explanation:

Given equation,

`5^x=81.2`

Taking log on both sides,

`log 5^x = log (81.2)`

By using the property of log i.e.
`log a^b = b log a`

`x log 5 = log (81.2)`

`\implies x = (log (81.2))/(log 5)=2.731957\approx 2.7320`