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How do you solve $2 {log}_{5} x = {log}_{5} 9$ $2log_5x=log_5 9$ ?

1 Answer

Oct 15, 2016

$x = 3$ $x=3$

Explanation:

Remember the general relation:
$XXX {log}_{b} (a^{c}) = c \cdot {log}_{b} (a)$ $color(white)("XXX")log_b (a^c)=c * log_b (a)$

Therefore
$XXX 2 {log}_{5} (x) = {log}_{5} (x^{2}) = {log}_{5} (9)$ $color(white)("XXX")2log_5(x)=log_5(x^2)=log_5(9)$

$XXX \to x^{2} = 9$ $color(white)("XXX")rarr x^2=9$

$XXX \to x = 3$ $color(white)("XXX")rarr x=3$ (since the argument of $log$ $log$ can not be negative)

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