Question

PLEASE ANSWER ASAP!!!!!!

Answer 1

Given:

$\bf{x^{\log_{4}3}+3^{\log_{4}x}=18}$

To Find:

• Value of x

Solution:

We know that,

$\rightarrow\sf{a^{\log_{m}b}=b^{\log_{m}a},where\:m>0,m\neq1,a>0,b>0}$

$\rightarrow\sf{If\log_{m}a=b,then\:a=m^{b},where\:m>0,m\neq1,a>0}$

$\rightarrow\sf{3^{2}=9}$

Now,

$\longrightarrow\sf{x^{\log_{4}3}+3^{\log_{4}x}=18}$

$\longrightarrow\sf{3^{\log_{4}x}+3^{\log_{4}x}=18}$

$\longrightarrow\sf{2\times3^{\log_{4}x}=18}$

$\longrightarrow\sf{3^{\log_{4}x}=\dfrac{\cancel{18}}{\cancel{2}}}$

$\longrightarrow\sf{3^{\log_{4}x}=9}$

$\longrightarrow\sf{3^{\log_{4}x}=3^{2}}$

On comparing power of 3 on both the sides, we get

$\longrightarrow\sf{\log_{4}x=2}$

$\longrightarrow\sf{x=4^{2}}$

$\longrightarrow\sf\pink{x=16}$

Hence, the value of x is 16.