How do you solve ${log}_{3} x = 5 {log}_{10} 2$ $log_3 x=5log_10 2$ ?

Question

1685 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-01T21:51:10

$x = 3^{{log}_{10} 32}$ $x=3^(log_10 32)$

Rewrite as:

${log}_{3} x = {log}_{10} (2^{5})$ $log_3x=log_10 (2^5)$

${log}_{3} x = {log}_{10} 32$ $log_3x=log_10 32$

$3^{{log}_{3} x} = 3^{{log}_{10} 32}$ $3^(log_3x)=3^(log_10 32)$

$x = 3^{{log}_{10} 32}$ $x=3^(log_10 32)$

$x \approx 5.226$ $x~~5.226$

How do you solve log_3 x=5log_10 2log3x=5log102log_3 x=5log_10 2?