AP Precalculus solving exponential and logarithmic equations quiz quiz

Graph the equation

Square both sides

Check whether both sides can be written with the same base

Take the logarithm of both sides immediately

$16$

$4$

$5$

$6$

$2$

$\frac{1}{2}$

$\frac{4}{3}$

$\frac{3}{4}$

Add the same value to both sides

Take a logarithm of both sides and apply the power property

Exponentiate both sides

Multiply both sides by the base

$x = \frac{\ln 50}{\ln 7}$

$x = 50 - 7$

$x = \frac{50}{7}$

$x = \ln 50 - \ln 7$

Divide every term by the base

Exponentiate immediately

Take another logarithm

Condense to a single logarithm using the log properties

$10$

$32$

$25$

$\frac{5}{2}$

Because logarithms are always negative

Because a logarithm requires a positive argument, so some candidates are not in the domain

Because squaring can introduce extra roots

Because the base might be negative

$x = 4$ only

$x = -2$ only

$x = 4$ and $x = -2$

No solution

$x = 2$

$x = 2e$

$x = \ln 2$

$x = e^2$

It becomes an equation

It is always undefined

It reverses

It is preserved, and you also intersect with the domain

The exam awards the method and justification, not only the final value

Logarithms cannot be solved by hand

Numerical answers are never accepted

You must always use a calculator