Logarithm #2.

Algebra Level 1

Given that log a 20736 = 4 \log_a 20736 = 4 and log b 42875 = 3 , \log_{b} 42875 =3, find 2018 a b 2018a -b


The answer is 24181.

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1 solution

Matin Naseri
Jan 15, 2018

My proof.

log a b = c \log_a{b=c} . For find a \large{a} we prove it b c = a \sqrt[c]{b}={a} .

then 20736 4 \sqrt[4]{20736} = \large{=} a 1 = 12 \large{a_1=12} .

42875 3 \sqrt[3]{42875} = \large{=} a 2 = 35 \large{a_2=35} .

( 2018 × 12 ) \large{(2018×12)} = 24216 35 = 24181 \large=24216-35=24181 .

N o t e = \large{Note=} a 1 \large{a_1} is b \large{b} in problem.

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