Prove that $\log _b \frac{u}{v}=\log _b u-\log _b v$.

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $\ln x+\ln (x-2)=1$

Evaluate log7 7^-0.89

Solve for $\boldsymbol{x}$. \

$$e^x=6$$

determine whether the statement is true or false given that f(x) = ln x. Justify your answer. If f(x) < 0, then 0 < x < 1

solve the logarithmic equation algebraically. Approximate the result to three decimal places. ln √x-8 = 5

determine whether the statement is true or false given that f(x) = ln x. Justify your answer. If

$$f(u) = 2f(v)$$

,then

$$v= u^2$$

solve for x. ln x = 4, e^x = 3

In this exercise, solve the exponential equation. Approximate your result to three decimal places.

$$14 e^{3 x+2}=560$$

In Exercise, graph the exponential function.

$$f(x)=-3^x+4$$

determine whether the statement is true or false given that f(x) = ln x. Justify your answer.

$$√f(x) = 1/2 f(x).$$

In this exercise, sketch the graph of the equation.

$$x^2+(y-8)^2=25$$

Solve for $\boldsymbol{x}$.
$5^x=\dfrac{1}{25}$

In this exercise, solve the exponential equation. Approximate your result to three decimal places.

$$3 e^{-5 x}=132$$