Solving Exponential Equations

What is the base?

• 3

• 7

• -3

• -7

What is the exponent?

• 1

• 2

• 8

• 1/8

Rewrite in Logarithmic Form:

5^x = 125

• log ₅ 125 = x

• log _x 125 = 5

• log ₅ x =125

• log₁₂₅ x = 5

Solve for x:

log ₅ 125 = x

• x = 3

• x = 2

• x ≈ 2.097

• x = 5

Rewrite in logarithmic form

• log ₇ 20 = x+2

• log ₇ 20 = x

• log ₂₀ x+2 = 7

• log _x+2 20 = 7

Rewrite the equation to have x by itself

• log ₇ (20) - 2 = x

• log ₇ (20) + 2 = x

• log ₇ (20 + 2) = x

• log ₇ (20 - 2) = x

Solve for x

• x ≈ -0.460

• x ≈ -0.461

• x ≈ 1.485

• x ≈ 1.486

Isolate the exponential term

• 3^x = 6

• 3^x = 12

• 2^x = 6

• 2^x = 12

Rewrite in logarithmic form

• log₃ 6 = x

• log₆ 3 = x

• log_x 6 = 3

• log₆ x = 3

Solve for x

• x ≈ 1.631

• x ≈ 2.262

• x ≈ 0.477

• x ≈ 0.778