Expand the logarithmic expression log((x^3*y^4)/(z^6))

 Exercise

$\log\left(\frac{x^3y^4}{z^6}\right)$

 

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

$\log \left(x^3y^4\right)-\log \left(z^6\right)$

 

Use the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$, where $M=x^3$ and $N=y^4$

$\log \left(x^3\right)+\log \left(y^4\right)-\log \left(z^6\right)$

 

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$3\log \left(x\right)+\log \left(y^4\right)-\log \left(z^6\right)$

 

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$3\log \left(x\right)+4\log \left(y\right)-\log \left(z^6\right)$

 

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$3\log \left(x\right)+4\log \left(y\right)-6\log \left(z\right)$

$3\log \left(x\right)+4\log \left(y\right)-6\log \left(z\right)$

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