Exponential & Logarithm Functions

Logarithm Equations

100

Solve.

log₄(5x+7) = log₄(2x + 31)

x = 8

200

Solve.

log₂(9m+2) = 7

m = 14

300

Solve. 

(1/2)log₈36 + log₈(3k+7) = log₈132

k = 5

400

Solve.

log(4p-2) = log(-5p+5)

p = 0.7778

500

Solve.

ln(p² - p) = ln(6p +18)

p = 9 , p = -2

Exponential Equations

100

Solve. 

64^x+7 = 4^5x-3

x = 12

200

Solve.

9^w-8 = (1/27)^2w

w = 2

300

Solve.

9ⁿ⁺¹⁰ + 3 = 81

n = -8.0172

400

Solve.

11^n-8 - 5 = 54

n = 9.7005

500

Solve.

8^n-5 = 48

n = 6.8617

Base "e" & Natural Log

100

Convert to logarithmic form.

e^x+5 = 72

ln72 = x+5

200

Convert to exponential form.

ln(x-9) = 32

e³² = x-9

300

Condense.

(1/3)ln64 + 2lnx

ln4x²

400

Expand.

ln(a³/b)²

6ln a - 2ln b 

500

Solve.

lnx - ln9 = 7

x = 9869.6984

Logarithm Equations

100

Solve. 

log5x = log(2x+9)

x = 3

200

Solve.

log(10-4x) = log(10-3x)

x = 0

300

log₁₂(v²+35) = log₁₂(-12v - 1)

v = -6

400

2logm = log36

m = 6

500

Solve.

2log(y+5) = log20 - log5

y = -3

Exponential Equations

100

6ⁿ = 99

n = 2.5646

200

Solve. 

2^3a = 142

a = 2.3832

300

Solve.

8^-5a - 5 = 53

a = -0.3905

400

(5)6^3m = 20

m = 0.2579

500

Solve.

(2)3^4y - 11 = 61

y = 0.8155