3.4-3.6 Review
Name___________________________________
Pre-Calculus
Period __________ Date ___________________
Assuming all variables are positive, use properties of
logarithms to write the expression as a sum or difference
of logarithms or multiples of logarithms.
1) log2 (xy)
A) log2 x + log2 y
B) log1 x - log1 y
C) log2 x - log2 y
2) log5
7) 4(8 - 2x) = 256
A) x = -2
C) x = 2
Solve the equation.
8) log 3 x = log 4 + log (x - 5 )
20
A) B) -20
7
D) log1 x + log1 y
2 x
y
A) log5 y - log5 2 -
C) 20
1
log5 x
2
1
log5 x - log5 y
2
1
D) log5 2 · log5 x ÷ log5 y
2
Solve the problem.
11) Assume the cost of a gallon of milk is $2.50.
With continuous compounding, find the time it
would take the cost to be 5 times as much (to
the nearest tenth of a year), at an annual
inflation rate of 6%.
A) 26.8 years
B) 0.1 years
C) 9.9 years
D) 0.0 years
D) log(x6 + y7)
4) 2 logm y - 3 logm z 2
A) logm
y2
z6
B) logm
2y
3z 2
C) logm
y2
2z 3
D) logm
y2
z5
12) At what interest rate must $5400 be
compounded annually to equal $12,590.85 after
11 yr? (Round to the nearest percent.)
A) 9%
B) 7%
C) 8%
D) 10%
Use the change of base rule to find the logarithm to four
decimal places.
18
5) log
8.6
A) 0.7445
B) 2.0930
C) 1.3433
D) 1.2553
Find the exact solution to the equation.
6) log x = - 2
1
A) x =
B) x = 20
2 10
C) x =
1
100
1
2
Find the amount accumulated after investing a principal P
for t years at an interest rate r.
10) P = $1,000, t = 2, r = 3%, compounded
semiannually (k = 2)
A) $1045.68
B) $1060.90
C) $61.36
D) $1061.36
Use the product, quotient, and power rules of logarithms
to rewrite the expression as a single logarithm. Assume
that all variables represent positive real numbers.
3) 6log x + 7log y
A) log(6x + 7y)
B) log (x6y7 )
C) log(42xy)
D) -
9) log4 (2x + 5) - log4(x - 2) = 1
A) 3.125
B) 6.5
C) 2.408
D) No solution
B) log5 (2 x) - log5 y
C) log5 2 +
B) x = 4
D) x = 64
D) x = -20
1