Condense the logarithmic expression log(x)+log(1)-8log(y+2)

 Exercise

$\log\left(x\right)+\log\left(1\right)-8\:\log\left(y+2\right)$

 

Evaluating the logarithm of base $10$ of $1$

$\log \left(x\right)+0-8\log \left(y+2\right)$

 

$x+0=x$, where $x$ is any expression

$\log \left(x\right)-8\log \left(y+2\right)$

 

Using the power rule of logarithms: $n\log_b(a)=\log_b(a^n)$

$\log \left(x\right)-\log \left(\left(y+2\right)^{8}\right)$

 

The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

$\log \left(\frac{x}{\left(y+2\right)^{8}}\right)$

$\log \left(\frac{x}{\left(y+2\right)^{8}}\right)$

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