# MATH 104 Algebra Applications

**Question description**

Write the equations in logarithmic form.

(a)

343 = 7^{3}

(b)

81 = (1/9 ninth) -2 square

(c)

*a* = *b ^{c}*

Use the definition of logarithm to simplify each expression.

(a)

log_{10} 10

(b)

log_{10} 100

(c)

log_{10} 10^{?3}

Solve each exponential equation. Give the exact value for*x*.

(a)

7* ^{x}* = 1/49 (1 over 49)

*x* =

(b)

5* ^{x}* = 8

*x* =

(c)

4* ^{x}* = 2.5

*x* =

(d)

2* ^{x}* = 3

*x* =

Find a simplified value for *x* by inspection. Do not use a calculator.

(a)

log_{7} 49 = *x*

*x* =

(b)

log_{2} 16 = *x*

*x* =

(c)

log_{3} 81 = *x*

*x* =

(d)

log_{4} 64 = *x*

*x* =

Contract the expressions. That is, use the properties of logarithms to write each expression as a single logarithm with a coefficient of 1.

(a)

ln 3 - 2 ln 8 + ln 16

(b)

ln 3 - 2 ln(6 + 9)

(c)

ln 3 - 2(ln 4 + ln 8)

A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of

5.2 10^{2}µm. Find this earthquake's magnitude. (Round your answer to one decimal place.)

Find the future value, using the future value formula and a calculator. (Round your answer to the nearest cent.)

$735 at 5.5% compounded quarterly for 4 years

$

Suppose that an insurance agent offers you a policy that will provide you with a yearly income of $80,000 in 30 years. What is the comparable salary today, assuming an inflation rate of 4% compounded annually? (Round your answer to the nearest cent.)

$

Convert the credit card rate to the APR.

Oregon, 1 and ¾ % per month

%

Assume the car can be purchased for 0% down for 60 months (in lieu of rebate).

A car with a sticker price of $42,950 with factory and dealer rebates of $5,100

(a) Find the monthly payment if financed for 60 months at 0% APR. (Round your answer to the nearest cent.)

$

(b) Find the monthly payment if financed at 2.5% add-on interest for 60 months. (Round your answer to the nearest cent.)

$

(c) Use the APR approximation formula to find the APR for part (b). (Round your answer to one decimal place.)

%

(d) State whether the 0% APR or the 2.5% add-on rate should be preferred.

0% APR or 2.5% add-on rate

Find the monthly payment for the loan. (Round your answer to the nearest cent.)

$700 loan for 12 months at 12%

$

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