50 followers problem!

Algebra Level 2

$3+ \log_2 x = \log_2 5$ If the value of $x$ can be represented as $\dfrac{p}{q}$ , where $p$ and $q$ are coprime positive integers, find $p+q$ .

1 solution

Rishik Jain
Jan 5, 2016

$\log_2 5 - \log_2 x = 3$

$\log_{2}{\left( \dfrac{5}{x} \right)} = 3$

$\because 2^3 = 8$

$\dfrac{5}{x} = 8$

$x = \dfrac{5}{8}$

$5$ and $8$ are co-prime integers.

$\therefore 5+8 = \boxed{13}$

How did you came to 2nd line from 1st line??

Sagar Shah - 5 years, 5 months ago

This is a property of Logarithms $\log_a b - \log_a c = \log_a{\left (\frac{b}{c} \right)}$

Rishik Jain - 5 years, 5 months ago