Evaluating and solving logarithims
log3(3x+6)=log312
A- X=2
B- X=10
C- X=3
D- X=5
What is A - X=2
REMEBER, same base -> set equal
(3x+6)=12 - minus 6 from both sides
3x=6 - dive by 3 both sides
x=2 - answer
Condense the log and choose the correct answer!
log r + k log q
a. log r / log qk
b. log rqk
c. log rkq
d. r log / log kq
The correct answers is:
b. log rq4
- Because of log rules addition problems turn into multiplication
- and because of exponential powers q goes to the power of k
Expand the logarithm fully using the properties of logs. Express the final answer in terms of log, logx.
a. 9 log - x log 3
b. log 9 + 3 log x
c. log 9 + x log 3
b. log 9 + 3 log x
log 9 + log x3
In Bx, what does B stand for?
Base
Sarah deposits $800 into a savings account that earns 5% interest per year. How much money will she have after 6 years?
a. A≈1123.567
b. t≈1072.087
c. A≈1072.087
d. t≈1123.567
What is, C - A≈1072.087
Work for Problem:
A=P(1+r)^t
P=800
r=5 - 5/100= 0.05
t=6
A= ?
A=800(1+0.05)^6 - A=800(1.05)^6
800x(1.05)^6 =
A≈1072.087
Solve for X:
32x+2 = 27
What is X=1/2
Remeber you can only set equal if you have the same base.
27= 33 -> 32x+2 = 33 - same base, set equal
2x+2 = 3 - subtract 2 from both sides
2x = 1 - divide 2 by both sides
x= 1/2
Condense the log!
b log x - 4 log r
What is...
log xb / r4
- Because of log rules subtraction turns into division
- Due to powers x is to the power of b and r is to the power of 4
Expand the log:
log x4 y3
What is...
4 log x + 3 log y
1. The power rule says to put the exponent in front of log and the variable after. Addition sign means multiplying.
What is the Compound Interest formula?
What is, A=P(l+r)t
Jake deposits $500 into an account earning 4% interest per year.
How long will it take for the account to grow to $700?
a. t≈8.579 years
b. A≈8.579
c. t≈10.346 years
d. A≈10.346
What is, A - t≈8.579 years
Work for Problem:
A=P(1+r)^t
A=700
P=500
r=4 - 4/100= 0.04
t=?
700=500(1+0.04)^t - 700=500(1.04)^t
Divide by 500 on both sides
1.4 =(1.04)^t - log(1.04)1.4=t (1.04 is the base)
log(1.4)/log(1.04)=t
t≈8.579 years
Solve for X:
log6(2x+5) = 3
What is X= 211/2
log6 (2x+5) = 3 -> 63 = 2x+ 5
216 =2x+5 - subtract 5 from both sides
211=2x - dived by 2 both sides
x=211/2
Condense the log!
log z + q log k
What is...
log zkq
- Because of the log principle addition turns into multiplication
-Because of powers k would be to the power of q
Expand the log:
log (x2y/5)
What is...
2 log x + log y - log 5
1. Use the power rule
2. Addition sign means multiplying, subtraction sign means dividing.
What is the change of base formula?
What is, logb A=log(a)/log(b)
An account grows to $1,800 after 7 years at 6% interest. What was the starting investment?
What is, P≈1197.103
Work for Problem:
A=P(1+r)^t
A=1800
r=6 - 6/100=0.06
t=7
P=?
1800=P(1+0.06)^7 - 1800=P(1.06)^7
Divide both sides by (1.06)^7
I would plug in 1.06^7 in the calculator, then divide it by 1800
P≈1197.103
Solve for X:
log8(2x+2)+4 = 6
What is X = 31
log8(2x+2) = 2 -subtracted the four from both sides, then set to expontential form
82 = 2x + 2
64 = 2x + 2 -subtarct 2 from both sides
62 = 2x - divde by 2 both sides
x = 31
Condense the log!
2 log4 x - 12 log4 y
What is...
log4 x2/y12
- Because of the principle of logs subtraction turns into division
- Because of powers x would be to the power of 2 and y to the power of 12
Expand the log:
log (5abz/2)
What is...
log 5 + log a + z log b - log 2
1. Use the power rule
What is the quotient rule?
What is...
logb (m/n) =
logb m - logb n
A person invests $2,500 at 3.5% interest per year.
How much will the investment be worth after 12 years?
What is, A≈3777.672
Work for Problem:
A=P(1+r)^t
P=2500
r=3.5 - 3.5/100=0.035
t=12
A=?
A=2500(1+0.035)^12 - 2500=(1.035)^12
1.035^12= 1.511069
A=2500x1.511069
A≈3777.672
Solve for X:
6 + log4x + 16 = 9
What is X = 4-13 or 1/67,108,864
- combine 16+6= 22
log4x +22 = 9 -subtract 22 from both sides
log4x = -13 -put into exponetial equations
4-13= X or solve 1/67,108,864 = X
Condense the log!
log4 x7 - log4 x2 + 4 log4 x3
What is...
log4 x7/x2 * x12
-Because of the law of logs subtraction turns into division and addition turns to subtraction
- With the principles of power x goes to the power of 7, x goes to the power of 2, and x to the power of 12
Expand the log:
log ((x4y3)/(2z2))
What is...
4 log x + 3 log y - log 2 - 2 log z
1. Use the power rule
What is the Power rule?
What is...
logb mn =
N logb m
Alex wants to save money for a car. He invests $1,200 in an account that earns 8% interest per year. He plans to buy a car that costs $5,000.
How long will it take for his investment to reach $5,000?
What is, t≈18.543 years
Work for Problem:
A=P(1+r)^t
P=1200
A=5000
r=8 - 8/100= 0.08
t=?
5000=1200(1+0.08)^t - 5000=1200(1.08)^t
Divide by 1200 on both sides
4.1667≈(1.08)^t log(1.08)4.1667=t
(1.08 is the base)
log(4.1667)/log(1.08)
t≈18.543 years