Question

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

Answer 1

`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`

Answer 2

`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`