How do you simplify ln(e^4x^(3t))?

Dec 15, 2015

$4 + 3 t \ln \left(x\right)$

Explanation:

Use the logarithm rule: ${\log}_{a} \left(b c\right) = {\log}_{a} b + {\log}_{a} c$

$\ln \left({e}^{4} {x}^{3 t}\right) = \ln \left({e}^{4}\right) + \ln \left({x}^{3 t}\right)$

Now, use the logarithm rule: ${\log}_{a} \left({b}^{c}\right) = c \cdot {\log}_{a} b$

$4 \ln \left(e\right) + 3 t \ln \left(x\right)$

Remember that $\ln \left(e\right) = 1$.

$4 + 3 t \ln \left(x\right)$