Solve for x.

Write the exact answer using either

base-10 or base-e logarithms.

$$11^{-9x}=18^{5+x}$$

An amount of 42,000 is borrowed for 5 years at 3% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?

Round your answer to the nearest dollar.

A principal of $3300 is invested at 7.25% interest, compounded annually. How many years will it take to accumulate $5000 or more in the account?

Write the smallest possible whole number answer.

Evaluate.

$$\log_9\ \frac{1}{81}$$

Solve for x. Simplify your answer as much as possible.

$$\log_{32}x=\frac{1}{5}$$

Write the expression as a single logarithm.

$$7\log_{b\ }\left(3y+1\right)+\frac{1}{5}\log_b\left(y+8\right)$$

Solve for the variable in the equation below. Round your answer to the nearest hundredth.

$$e^y=12$$

Fill in the missing value to make the equation true.

Fill in the missing value to make the equation true.

Fill in the missing value to make the equation true.

Use the properties of logarithms to expand the logarithm below. Each logarithm should involve only one variable and not have any exponents.

$$\log_4\left(\frac{x}{z^3}\right)$$

Rewrite as a logarithmic equation.

$$e^5=x$$

Solve for x.

$$\log_2\left(-6-2x\right)=2$$

Solve for x. Do not round any intermediate computations, and round your answer to the nearest hundredth.

$$3\ln\left(x+3\right)=-6$$

Solve for x.

$$\ln6+\ln\left(x-1\right)=\ln x$$