Question

\[\log_{21}(x-84)=3-\log_{21}x\] solve

Answer 1

\[\log_{21}(x-84)=3-\log_{21}x \]
\[\log_{21}(x-84)=\log_{21}21^3-\log_{21}x \]
\[\log_{21}(x-84) =\log_{21}\frac{9261}{x} \]
\[x-84=\frac{9261}{x}\]
\[x^2-84x-9261=0\]
\[(x-147)(x+63)=0\]
\[x=147, -63\]

Answer 2

Discard -63 as it causes a negative argument

Answer 3

Thank you for writing this out! Which rule is used changing the "3?"

Answer 4

Well, actually I made it harder than it is. Try this: Add log base 21 of x to both sides and then use the first law of logs to write it as a product

Answer 5

\[\log_{21}(x-84)+\log_{21}x=3 \]
\[\log_{21}(x-84)(x)=3 \]
\[\log_{21}(x^2-84x)=3\]
\[21^3=x^2-84x\]
\[x^2-84x-9261=0\]

Answer 6

\[Log _{a} a = 1 \]

Answer 7

There you go.

Answer 8

Thank you. :-)

Answer 9

yw