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Solve for x using properties of logarithms: log2(32)-log3(x)=log5(25)?

2 Answers

Feb 22, 2018

$x=1$

Explanation:

Since $2^5=3color(white)("xx")harrcolor(white)("xx")log_2(32)=5$
and $color(white)("x")5^2=25color(white)("xx")harrcolor(white)("xx")log_5(25)=2$

$log_2(32)-log_3(x)=log_5(25)$
is equivalent to
$5-log_3(x)=2$

$rArr log_3(x)=3$
and
since $3^color(blue)1=3$
$color(white)("XXX")log_3(x)=3color(white)("xx")rarrcolor(white)("xx")x=color(blue)1$

Feb 22, 2018

$x=27$

Explanation:

$log_2(32)-log_3(x)=log_5(25)$

$log_2(2^5)-log_3(x)=log_5(5^2)$

$5log_2(2)-log_3(x)=2log_5(5)$

$5-log_3(x)=2$

$log_3(x)=3$

Hence $x=3^3=27$

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