Question

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

Answer 1

Answer:

The value of x is 2.7320 ( approx )

Step-by-step 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. $log a^b = b log a$

$x log 5 = log (81.2)$

$\implies x = \frac{log (81.2)}{log 5}=2.731957\approx 2.7320$

Answer 2

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)