Convert the following exponential expression to its equivalent logarithmic form.
$3^{x}=7$

ln x is unbounded Use the following argument to show that lim (x → ∞) ln x = ∞ and lim (x → 0⁺) ln x = −∞.

c. Show that ln 2ⁿ > n/2 and ln 2^(−n) < −n/2.

Convert the following logarithmic expression to its equivalent exponential form.

$\(\log\)_4x=5$

Convert the following logarithmic expression to its equivalent exponential form.

$x=\(\log\)9$

Convert the following exponential expression to its equivalent logarithmic form.

$e^9=x+3$

{Use of Tech} Let f(x) = ln((x+1)/(x-1)) and g(x) = ln ((x+1)/(x-1)).

b. Sketch graphs of f and g to show that these functions do not differ by a constant.

Convert the following expressions to the indicated base.

$2^x$ using base e