Question

Evaluate3^(2-log_(3)4)​

Answer 1

Topic :-

Logarithm

Given :-

$3^{(2-\log_34)}$

To Find :-

Simplified value of given expression.

Solution :-

$3^{(2-\log_34)}$

$3^{(\log_39-\log_34)}$

$\left (\because \log_39=2 \right )$

$3^{(\log_3(9/4))}$

$\left (\because \log_am - \log_an=\log(m/n) \right )$

$(9/4)^{(\log_33)}$

$\left (\because a^{\log m}=m^{\log a} \right )$

$\left ( \dfrac{9}{4} \right)^1$

$\left (\because \log_aa=1 \right )$

$\left ( \dfrac{9}{4} \right)$

Answer :-

So, simplified value of given expression is 9/4 = 2.25.

Note :

In such type of questions, we generally try to manipulate powers so that it can be easily simplified using some properties of Logarithm.

You may use base of Logarithm for manipulation.