Question

pre - calculus cp ic 25 - 26
exponential and logarithmic equations
verting between exponential and lo
the equation $e^x = 2x$ is equivalent to

Explanation:

Step1: Recall conversion rule

The conversion rule from exponential form $a^b = c$ to logarithmic form is $\log_a c=b$. For the equation $e^x = 2x$, taking the natural - logarithm (since the base of the exponential is $e$) of both sides gives $\ln(e^x)=\ln(2x)$.

Step2: Simplify left - hand side

Using the property $\ln(e^y)=y$ for any real number $y$, the left - hand side $\ln(e^x)$ simplifies to $x$. So the equivalent equation is $x = \ln(2x)$.

Answer:

$x=\ln(2x)$