7-5
7-5
Exponential and Logarithmic
Solving Logarithms
Equations and Inequalities
Solve.
4x – 1 = 5
log 4x – 1 = log 5
(x – 1)log 4 = log 5
log5
x –1 = log4
5 is not a power of 4, so take the
log of both sides.
Apply the Power Property of
Logarithms.
Divide both sides by log 4.
log5
x = 1 + log4 ≈ 2.161
Check Use a calculator.
The solution is x ≈ 2.161.
Holt Algebra 2
7-5
7-5
Exponential and Logarithmic
Solving Logarithms
Equations and Inequalities
Solve.
23x+1 = 32x
ln23x+1 = ln32x
3 is not a power of 2, so take the ln
of both sides.
(3x+1)ln2 = (2x)ln3
Apply the Power Property of
Logarithms.
3xln2 + ln2 = (2x)ln3
Divide both sides by 2x, then
divide both sides by log2.
3xln2 – 2xln3 = -ln2
x(3ln2 – 2ln3) = -ln2
x=
−𝑙𝑛2
3𝑙𝑛2−2𝑙𝑛3
Holt Algebra 2
≈ 5.885
7-5
7-5
Exponential and Logarithmic
Solving Logarithms
Equations and Inequalities
Solve.
52x+1 = 7x–3
ln52x+1 = ln7x–3
(2x+1)ln5 = (x-3)ln7
5 is not a power of 7, so take the
log of both sides.
Apply the Power Property of
Logarithms.
2xln5 + ln5 = xln7 – 3ln7
Distribute.
2xln5 – xln7 = –3ln7 – ln5
Group like terms.
x(2ln5 – ln7) = -3ln7 – ln5
x=
−3𝑙𝑛7−𝑙𝑛5
2𝑙𝑛5−𝑙𝑛7
Holt Algebra 2
≈ -5.850
7-5
7-5
Exponential and Logarithmic
Solving Logarithms
Equations and Inequalities
Solve.
83 – x = 2∙54x
ln83–x = ln(2∙54x)
(3-x)ln8 = ln2 + ln54x
(3-x)ln8 = ln2 + 4xln5
5 is not a power of 8, so take the
log of both sides.
Apply the Power Property of
Logarithms.
-xln8 + 3ln8 = ln2 + 4xln5
Distribute.
3ln8 – ln2 = 4xln5 + xln8
Group like terms.
ln512 – ln2 = xln625 + xln8
ln256 = x(ln625 + ln8)
x=
𝑙𝑛256
𝑙𝑛625+𝑙𝑛8
Holt Algebra 2
≈ 0.651
7-5
Exponential and Logarithmic
Equations and Inequalities
Homework Exp & Log Worksheet on Homeroom
Do all 3 questions sets.
Holt Algebra 2