Answer
a. $\log_{a}x=y \Leftrightarrow a^{y}=x$, see step-by-step
b. logarithm with base $e$
c. logarithm with base 10
d. $7^{2}=49$
Work Step by Step
a.
The logarithmic function $\log_{a}$ with base $a ($where $a>0, a\neq 1)$
is defined for $x > 0$ by
$\log_{a}x=y \Leftrightarrow a^{y}=x$
( $\log_{a}x$ is the exponent to which the base $a$ must be raised to give $x$)
b.
The natural logarithm is the logarithm with base $e.$
c.
The common logarithm is the logarithm with base 10.
d.
$\log_{a}x=y \Leftrightarrow a^{y}=x$
$\log_{7}49=2$ , the logarithmic form, is equivalent to
$7^{2}=49$, the exponential form.