Question

how can i solve this above question ?

$log_{8}(log_{2}( log_{3}(4 {x}^{} + 17) ) ) = 1 \div 3$

Answer 1

Hi...☺

Here is your answer...✌

We know that,

$log_{a}(b) = p \\ \\ = > b = {a}^{p}$

Now,

$log_{8}(log_{2}( log_{3}(4 {x} + 17) ) ) = \frac{1}{3} \\ \\ = > log_{2}( log_{3}(4 {x} + 17) = {8}^{ \frac{1}{3} } \\ \\ log_{2}( log_{3}(4 {x}+ 17) = {( {2}^{3} )}^{ \frac{1}{3}} \\ \\ log_{2}( log_{3}(4 {x}+ 17) = 2 \\ \\ = > log_{3}(4 {x}+ 17) = {2}^{2} \\ \\ log_{3}(4 {x}+ 17 )= 4 \\ \\ = > 4x + 17 = {3}^{4} \\ \\ 4x = 81 - 17 \\ \\ 4x = 64 \\ \\ x = \frac{64}{4} \\ \\ = > x = 4$