Question

if $10^x = 5$, what is $x$?
$x = \frac{1}{2}$ $x = \ln 5$ $x = \log_{10} 5$

Explanation:

Step1: Recall the definition of logarithms

The logarithmic form of the exponential equation \(a^b = c\) is \(b=\log_a c\), where \(a>0,a
eq1\).

Step2: Apply the definition to the given equation

Given \(10^x = 5\), comparing with \(a^b = c\) (here \(a = 10\), \(b=x\), \(c = 5\)), by the definition of logarithms, we get \(x=\log_{10}5\).

Answer:

\(x=\log_{10}5\) (the option with this expression)