Exponential and Logarithmic Functions

Rewrite log_pt = m in exponential form.

• p^t = m
• t^m = p
• m^t = p
• p^m = t

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Solve for x:
2^x+6=2⁵

• -1
• 11
• 1
• -11

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

• 5
• -5
• 1/5
• -1/5

Solve for b:
36^3b = 216^b+4

• 6
• 1
• 4
• -4

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

Solve the following for 'x';
log₆(3x - 2) = log₆(5x - 8)

• x = 3
• x = 2
• x = -1
• No Solution

Solve for x.
e^x+6 + 5 = 1

• -4.614
• -4.236
• No Solution
• -0.334

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

• g(x)=log₃(x+6)+4

• g(x)=log₃(x+4)-6

• g(x)=log₃(x-6)+4

• g(x)=3log(x+6)+4