Please help logarithms!

Question

asked Jan 24, 2022 142k views

1 Answer

Dimoniy · Answer 1 · 2022-01-29T00:27:31+0000

Given:

$\log_34\approx 1.262$

$\log_37\approx 1.771$

To find:

The value of
$\log_3\left((4)/(49)\right)$ .

Solution:

We have,

$\log_34\approx 1.262$

$\log_37\approx 1.771$

Using properties of log, we get

$\log_3\left((4)/(49)\right)=\log_34-\log_349$
$\left[\because \log_a(m)/(n)=\log_am-\log_an\right]$

$\log_3\left((4)/(49)\right)=\log_34-\log_37^2$

$\log_3\left((4)/(49)\right)=\log_34-2\log_37$
$[\log x^n=n\log x]$

Substitute
$\log_34\approx 1.262$ and
$\log_37\approx 1.771$ .

$\log_3\left((4)/(49)\right)=1.262-2(1.771)$

$\log_3\left((4)/(49)\right)=1.262-3.542$

$\log_3\left((4)/(49)\right)=-2.28$

Therefore, the value of
$\log_3\left((4)/(49)\right)$ is
.