Exponential and Logarithmic Equations

Rewrite as a log: x = 11^y

• log₁₁(y) = x

• log_y(11) = x

• log₁₁(x) = y

• log_x(y) = 11

Find x: log₂(32) = x

• x = 5

• x = 16

• x = 4

• x = 6

Rewrite as an exponential:
log(10,000)=4.

• e⁴=10,000

• 4^10,000=10

• 10⁴=10,000

• 0⁴=10

Solve for x:
log₄(64)=x.

• 16

• 10

• 3

• 8

Solve.

9(e^x) - 31 =23

• x = 1.79

• x = 4.21

• x = -3.5

• x = 1.27

Solve.

2(16^x+6) - 8 = 35

• -4.67

• -4.89

• -2.93

• -2.95

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

• 5

• -2

• -5

• 2

Solve: 9^8-x = 27^x-3

• 5

• -5

• 1/5

• -1/5

Change to Exponential Form:
log₆36 = 2

• 2⁶=36

• 6²=36

• 36²=6

• 36⁶=2