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