Use the properties of logarithms to prove log, 1000 = log2 10.

Question

asked Sep 8, 2022 169k views

1 Answer

Embattled Swag · Answer 1 · 2022-09-14T07:11:44+0000

Given:

Consider the equation is:

$\log_81000=\log_210$

To prove:

$\log_81000=\log_210$ by using the properties of logarithms.

Solution:

We have,

$\log_81000=\log_210$

Taking left hand side (LHS), we get

$LHS=\log_81000$

$LHS=(\log 1000)/(\log 8)$
$\left[\because \log_ab=(\log_x a)/(\log_x b)\right]$

$LHS=(\log (10)^3)/(\log 2^3)$

$LHS=(3\log 10)/(3\log 2)$
$[\because \log x^n=n\log x]$

$LHS=(\log 10)/(\log 2)$

$LHS=\log_210$
$\left[\because \log_ab=(\log_x a)/(\log_x b)\right]$

LHS=RHS

Hence proved.