Question

Write 3log2-5log3+2log5 as a single logarithm

Answer 1

Given :

logarithmic expression = 3log2-5log3+2log5

To find :

Above expression in single logarithm

Solution :

Let us recall some log properties

• xlogy = log(y)^x

• logx + logy = log(xy)

• logx - logy = log(x/y)

Simplifying above expression

3log2 - 5log3 + 2log5

= log(2)^3 - log(3)^5 + log(5)^2

= log8 - log243 + log25

= log(8/243) + log25

= log(8 × 25/243)

= log( 400/243 )

Hence,

3log2 - 5log3 + 2log5 = log( 400/243 )