M4 5-6 Practice Solving Logarithmic Equations

Solve log(x) + log(x+3) = 1

Use the properties to write as one log statement. Common logs have an understood base of 10.

• 5

• -2

• -5

• 2

log₂(x + 2) + log₂x = 3

Use the properties to write as one log statement. Once you simplify the left side of the equation to a single log, write the equation in exponent form and solve.

• -4, 2

• -2, 4

• 2

• 1

log₅(4x-7)=log₅(x+5)

Because there is a log base 5 on both sides of the equation, set the ( ) = to each other and solve for x.

• 3

• 12

• 4

• 7

log₂(x+3)=4

Write the equation in exponent form and solve.

• 16

• 13

• 3

• 10

log₈(4x+4)=2

Write the equation in exponent form and solve.

• 15

• 12

• 10

• 3

3^{2x – 6} = 81

Get the bases alike and set the exponents equation to each and solve.

• x = log 4

• x = 5

• x = 4

• x = -1

7ⁿ⁺¹⁰- 8 = 6

Move the 8 to the right side of the equation. Write in log form and use the calculator to solve.

• -7.374

• -8.643

• -7.360

• -8.853

Solve for x:

5 e^6x+3 = 0.1

Move the loose terms to the right side of the equation and get the e-term alone. Take the Natural log (ln) of both sides. Remember ln e goes away and you use the exponent to solve. Use your calculator to solve.

• -1.152

• 0.232

• -3.077

• -0.854

3^{2x – 6} = 27

Get the bases alike and set the exponents equation to each and solve.

• x = 9/2

• x = 5

• x = 4

• x = -1

Solve.

9(e^x) - 31 =23

Move the loose terms to the right side of the equation and get the e-term alone. Take the Natural log (ln) of both sides. Remember ln e goes away and you use the exponent to solve. Use your calculator to solve.

• x = 1.79

• x = 4.21

• x = -3.5

• x = 1.27