Answer
a.) $x = 10$
b.) $x = 5$
Work Step by Step
$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$
a.) $\log_x 1000 = 3$
b.) $\log_x 25 = 2$
a.) $\log_x 1000 = 3$
Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$
$$\log_x 1000 = 3 \rightarrow x^3 = 1000$$
Rewrite 1000 as $10^3$ [Note: $10^3 = 10\times10\times10 = 1000$]
$$x^3 = 10^3$$
$$x = 10$$
b.) $\log_x 25 = 2$
Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$
$$\log_x 25 = 2 \rightarrow x^2 = 25$$
Rewrite 25 as $5^2$ [Note: $5^2 = 5\times5 = 25$]
$$x^2 = 5^2$$
$$x = 5$$
