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matrenka [14]
3 years ago
9

Use the properties of logarithms to expand the following expression as much as possible. simplify any numerical expressions that

can be evaluated without a calculator.
ln(6x9/y5) please show work. the 9 and 5 are both exponents. I don't know how to use this app yet
Mathematics
1 answer:
FinnZ [79.3K]3 years ago
8 0
\bf log_{{  a}}(xy)\implies log_{{  a}}(x)+log_{{  a}}(y)
\\ \quad \\\\
% Logarithm of rationals
log_{{  a}}\left(  \frac{x}{y}\right)\implies log_{{  a}}(x)-log_{{  a}}(y)
\\ \quad \\\\
% Logarithm of exponentials
log_{{  a}}\left( x^{{  b}} \right)\implies {{  b}}\cdot  log_{{  a}}(x)\\\\
-----------------------------\\\\
ln\left( \cfrac{6x^9}{y^5} \right)\implies ln(6x^9)-ln(y^5)\implies ln(6)+ln(x^9)-ln(y^5)
\\\\\\
ln(6)+9ln(x)-5ln(y)
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