Logarithms' challenger #4.The easiest!

Algebra Level 2

Evaluate: $\large{81^{\frac{1}{\log_{5}{3}}}}$

This problem is a part of this set .

None of these. 81 625 125 20

1 solution

Rohit Udaiwal
Oct 10, 2015

$81^{\frac{1}{\log_{5}{3}}}$ $=81^{\log_{3}{5}} =3^{\log_{3}{5}^{4}}=5^{4}=625$ .

For sake of veriety,
Using formula, $\color{#3D99F6}{ x = e^{ln x}} \ \forall \ x > 0$

$\Rightarrow 81^{\dfrac{1}{\log_5^{3}}}$

$\Rightarrow e^{\dfrac{\ln 5}{\ln 3} \cdot \ln 81}$

$\Rightarrow e^{4 \ln 5} = \boxed{625}$

Akhil Bansal - 5 years, 8 months ago

Great job sir!:)

Rohit Udaiwal - 5 years, 8 months ago