Logarithms' challenger #5

Algebra Level 2

If $4^{A}+9^{B}=10^{C}$ where $A=\log_{16}{4},B=\log_{3}{9}$ and $C=\log_{x}{83}$ ,Then find $x$ .

This problem is a part of this set .

1 solution

Swapnil Das
May 19, 2016

$A=\log _{ 16 }{ 4 } =\frac { 1 }{ 2 } \\ B=\log _{ 3 }{ 9 } =2$

$\Rightarrow { 4 }^{ 1/2 }+{ 9 }^{ 2 }={ 10 }^{ \log _{ x }{ 83 } }$

$\Rightarrow 2+81={ 83 }^{ \log _{ x }{ 10 } }\\ \Rightarrow \color\red{x=10}$

$\mathcal{NICE}$

Rohit Udaiwal - 5 years ago