Condense or Expand Logarithms
Condense into a single logarithm:
log212 + log27 + log25
log2420
Solve for x:
log (3x-2) = 2
34
Rewrite into exponential form:
log 10,000 = 4
104 = 10000
3x - 2 = 12
2.402
Larry invested $27,000 in a savings account that pays an annual interest rate of 1.8%. The savings account is set to compound quarterly. How much is in Larry’s account after 5 years?
$29,536.74
Expand:
log2(x3y)4
12 log2x + 4 log2y
Solve for y:
log5(3x - 8) = 2
11
Rewrite into logarithmic form:
53 = 125
log5125 = 3
31-x = 2
.369
Becky invested 19,800 in a CD that pays an annual interest rate of 5.3%. The CD is set to compound daily. How much is in Becky’s account after 9 years?
$31,901.32
Condense:
log310 - log32
log35
2 = log 2 + log (3x-4)
18
Rewrite using change of base formula:
log6216
log 216 / log 6
Evaluate:
log51.9
.399
Jake invests in an annuity with an annual fixed interest rate of 6.2%. The annuity compounds monthly. If after 10 years, the account balance is $27,839.45 how much was the beginning investment?
$15,000
Expand:
log6(u3 / v1/2)
3 log6u - 1/2 log6v
log x + log (x-1) = log (4x)
5 (0 is extraneous)
Evaluate the expression:
log442
2
Evaluate:
log3(1/7)
-1.771
Jennifer is saving up for a house and wants $28,000 for a down payment. She will invest a lump sum into a savings account for 5 years that pays 4.3% annual interest and compounds monthly. How much should she put in the savings account?
$22,591.84
Solve for x:
3 logx2 - logx1 = 3
2
log9(x-5) + log9(x+3) = 1
6
Evaluate the expression:
log71
0
4 (3x) = 25
1.668
Melissa is investing money in National Bank and Trust. They are offering an account with an annual interest rate of 3.75%. This account will compound monthly. Assuming Melissa has $10,000 to invest, how long should she invest to make $16,029.39.
11.42 years