Convert to Logarithmic Form 0.5*e^(4z)=13

$0.5 \cdot e^{4 z} = 13$

Simplify.

Divide each term in $0.5 e^{4 z} = 13$ by $0.5$ .

$\frac{0.5 e^{4 z}}{0.5} = \frac{13}{0.5}$

Divide $13$ by $0.5$ .

$26$

Reduce by cancelling the common factors.

$e^{4 z} = 26$

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the right side $(26)$ equals the exponent $(4 z)$ .

$\log_{e} (26) = 4 z$