Final Answer
$x=\frac{8}{\ln\left(2\right)}$
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Step-by-step Solution
Problem to solve:
$\ln\left(2^x\right)=2^3$
Specify the solving method
1
Calculate the power $2^3$
$\ln\left(2^x\right)=8$
Learn how to solve logarithmic equations problems step by step online.
$\ln\left(2^x\right)=8$
Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation ln(2^x)=2^3. Calculate the power 2^3. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Eliminate the \ln\left(2\right) from the left side, multiplying both sides of the equation by the inverse of \ln\left(2\right). section:Verify that the solutions obtained are valid in the initial equation.
Final Answer
$x=\frac{8}{\ln\left(2\right)}$