Question

2^log18 base 6 ×3 ^log 3 base6

Answer 1

jai shree ram...

har har mahadev....

Answer 2

Answer:

Concept:

The logarithm is the exponent or power to which a base must be raised in order to produce a given number. If $b^{x}=n$, then x is the logarithm of n to the base b, which is expressed mathematically as $x=\log _{b} n$ .

Step-by-step explanation:

Given:

$\left(2^{\log _{6} 18}\right)\left(3^{\log _{6} 3}\right)$

Find:

$\left(2^{\log _{6} 18}\right)\left(3^{\log _{6} 3}\right)$

Solution:

$\begin{aligned}&\left(2^{\log _{6}^{6 \times 3}}\right)\left(3^{\log _{6}^{3}}\right) \\&\Rightarrow\left(2^{1+\log _{6}^{3}}\right)\left(3^{\log _{6}^{3}}\right) \\&\Rightarrow\left(2 \times 2^{\log _{6}^{3}}\right)\left(3^{\log _{6}^{3}}\right) \\&\Rightarrow 2(2 \times 3)^{\log _{6}^{3}} \\&\Rightarrow 2(6)^{\log _{6}^{3}} \\&\Rightarrow 2(3)^{\log _{6}^{6}} \\&\Rightarrow 2(3)^{1}=6\end{aligned}$

The Value is 6

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