Answer:
x ≈ 48.3177
Step-by-step explanation:
Using the rule of logarithms
log [tex]x^{n}[/tex] ⇔ n log x
Given
[tex](1.1)^{x}[/tex] = 100 ( take the log of both sides )
log[tex]1.1)^{x}[/tex] = log100 , then
x log1.1 = log100 ( divide both sides by log1.1 )
x = [tex]\frac{log100}{log1.1}[/tex] ≈ 48.3177 ( to 4 dec. places )
