Question

Find the value of x if (1.1)^x=100​

Answer 1

x ≈ 48.3177

Explanation:

Using the rule of logarithms

log
`x^(n)` ⇔ n log x

Given

`(1.1)^(x)` = 100 ( take the log of both sides )

log
`1.1)^(x)` = log100 , then

x log1.1 = log100 ( divide both sides by log1.1 )

x =
`(log100)/(log1.1)` ≈ 48.3177 ( to 4 dec. places )