Question

log 1000 base 0.1 evaluate the following​

Answer 1

Step-by-step explanation:

og

0.1

0.001

\text{This can be written as}This can be written as

=\log_{0.1}(0.1)^3=log

0.1

(0.1)

3

\text{Using quotient rule of logarithm}Using quotient rule of logarithm

\boxed{\bf\,log_aM^n=n\;log_aM}

log

a

M

n

=nlog

a

M

=3\,\log_{0.1}0.1=3log

0.1

0.1

\text{We know that, }\;\;\boxed{\bf\log_aa=1}We know that,

log

a

a=1

=3(1)=3(1)

Answer 2

$\huge{\mathcal{\underline{\green{SOLUTION}}}}$

$log_{0.1}(1000)$

$= \frac{ log(1000) }{ log(0.1) }$

$= \frac{ log( {10}^{3} ) }{ log( \frac{1}{10} ) }$

$= - 3 \times \frac{ log(10) }{ log(10) } = - 3$

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