The Universe Speaks Math-8

Algebra Level 2

H K J G F

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1 solution

Ram Mohith
Nov 9, 2018

log 5 x = log 2 24 log 2 3 = log 2 ( 24 3 ) ( Note that log a b l o g a c = log a b c ) = log 2 8 = 3 log 2 2 log 5 x = 3 x = 5 3 = 125 \begin{aligned} \log_5 x & = \log_2 24 - \log_2 3 \\ & = \log_2 \left(\dfrac{24}{3} \right) \qquad \qquad \left({\color{#3D99F6} \text{Note that } \log_a b - log_a c = \log_a \dfrac{b}{c}}\right) \\ & = \log_2 8 \\ & = 3 \log_2 2 \\ \implies \log_5 x & = 3 \\ \implies & \boxed{x = 5^3 = 125} \\ \end{aligned}

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