Write the equation in logarithmic form. (1/3)^3=1/27

Question

asked Jul 16, 2020 148k views

2 Answers

Aleksandrenko · Answer 1 · 2020-07-20T08:21:29+0000

Answer:

$\log_{(1)/(3)} ((1)/(27))=3$

Explanation:

The given equation is

((1)/(3))^3=(1)/(27)

We need to write the equation in logarithmic form.

Taking log on both sides.

$\log ((1)/(3))^3=\log ((1)/(27))$

Using the property of logarithm we get

$3\log ((1)/(3))=\log ((1)/(27))$
$[\because \log a^b=b\log a]$

Divide both sides by
$\log ((1)/(3))$ .

$3=(\log ((1)/(27)))/(\log ((1)/(3)))$

Using the property of logarithm we get

$3=\log_{(1)/(3)} ((1)/(27))$
$[\because \log_x y =(\log_ay)/(\log_ax)]$

Therefore, the logarithmic form of given equation is
$\log_{(1)/(3)} ((1)/(27))=3$ .