Question

Write In 6x¹0 - In 3x6

In 6x¹0 - In 3x8
10
(Simplify your answer.)
pourr
as a single term that does not contain a logarithm.
CHELSCENSE
RE
Categ
OERETR
TUTETEA
COLOR
FREEZE
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3. MEN FOGYA
B
AgateELEINE
INGREPE
LICENCE
Mobing
100
COL70:36
TULERE BE
OPREFERE

Answer 1

`\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad a^(log_a (x))=x\qquad \leftarrow \qquad \textit{we'll use this one} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ {\Large \begin{array}{llll} e^{\ln(6x^(10))~~ - ~~\ln(3x^6)} \end{array}} \\\\[-0.35em] ~\dotfill`

`\ln(6x^(10))~~ - ~~\ln(3x^6)\implies \ln\left( \cfrac{6x^(10)}{3x^6} \right)\implies \ln(2x^4) \\\\[-0.35em] ~\dotfill\\\\ e^{\ln(6x^(10))~~ - ~~\ln(3x^6)}\implies e^(\ln(2x^4))\implies e^(\log_e(2x^4))\implies \boxed{2x^4}`