Question

Show that log 1000=3log2+3log5

Answer 1

Answer:

LHS log 1000

RHS 3 log 2 + 3 log 5

> log 2^3 + log 5^3 [ n log m = log m^n ]

> log 8 + log 125. [ log m + log n = log(mn)

> log ( 8 * 125 )

> log 1000

> LHS hence proved

Answer 2

Concept:

This question requires basic knowledge of how to solve logarithmic functions.

The following formulas will be required.

1. $log(m^{n})=nlog(m)$

2.$log(m*n)=log(m)+log(n)$

Given:

The following equation is given:

log 1000=3 log2+ 3 log5

To prove:

We need to prove that

log 1000=3 log2+2 log5

Solution:

Now let's solve the RHS

log 1000

⇒$log10^{3}=3log(10)$

⇒$3log(5*2)=3(log2+log5)$

⇒3 log2+2 log5

Therefore LHS=RHS

Hence it is proved that

log 1000=3 log2+2 log5