Exponentials and Logarithms

Exponentials with Like Bases

100

4^5x=4¹⁰

What is 2

200

7^(x-5)=49^x

What is -5

300

64^(2x+4)=16^5x

What is x=3

400

(1/5)^x=125

What is x=-3

500

1/128=2^(5x+3)

What is x=-2

Exponentials with unlike bases

100

Solve for the variable: 3^b=17

What is 2.58

200

5*18^x=20

What is 0.48

300

e^(x-1)-5=5

What is 3.30

400

9ⁿ⁺¹⁰+3=81

What is -8.02

500

-6e⁸ⁿ⁺⁸-3=-23

What is -0.85

Condensing Logarithms

100

log (x) + log (y)

What is log (xy)

200

log (x) + log (y) - 3log(z)

What is xy/z³

300

2(ln(p)-ln(3))

What is (p/3)²

400

log₆(2)+log₆(3)= ?

What is 1

500

log₅(200)-log₅8=?

What is 2

Expanding Logarithms

100

log(ab³c)

What is log(a) + 3log(b)+log(c)

200

log_b(5)=0.774 log_b(12)=1.195 What is log_b(60)=?

What is 1.969

300

log_b(5)=0.774 log_b(12)=1.195 What is log_b(144)=?

What is 2.39?

400

log_b(5)=0.774 log_b(12)=1.195 What is log_b(2.4)=?

What is 0.421?

500

ln (sqrt(x)/y²)

What is 1/2ln(x)-2ln(y)

Solving Logarithms

100

Solve for x: log(2x)=2

What is 50

200

log₄64=x

What is x=3

300

Solve for x: log₅5³=x

What is 3?

400

ln e^4x=16

What is 4

500

ln 1 = x

What is 0