Question

Log 1/243 to the base 3

Answer 1

(3)x=243

log (3)x= log 243 ( take log)

x log 3 = log (3) 5

x log 3 = 5 log 3

x= 5

Answer 2

Answer:

- 5 .

Step-by-step explanation:

We have to simplify Log 1 / 243 to the base 3.

Here we will use log formula.

$\large log _ ax^m=m \ log _a x$

Rewrite 243 in power of 3

$\large 243=3\times 3 \times3\times3\times3\\\\\\\large 243=3^5$

$\large \text{We know \dfrac{1}{x} can be written as x^{-1} }$

So,

$\large log _ 3\dfrac{1}{243} \\\\\\\large log _ 33^{-5}\\\\\\\large -5log _ 33\\\\\\\large \text{We know log_xx=1 }\\\\\\\large -5log _ 33=-5\times1\\\\\\\large -5$

Thus we get answer - 5.