Exponents and Logs

Exponential Equations

100

Solve for x:

4^(x+3)=4^(2x-1)

x =4

200

Solve for x. 

2^(3x-1)=16^x

x=-1

300

Solve for x.

9^(x+2)=27^(2x-3)

x=13/4

400

Solve: 

2^x+7=62

Round to 2 decimal places

x= 5.78

500

Solve: 5^2x+1 = 31

Round to the nearest tenth.

x = 0.6

Exponent to Log

100

Rewrite in log form:

8² = 64

log₈64 = 2

200

Rewrite in log form:

17² = 289

log₁₇289 = 2

300

Rewrite in log form:

256^1/2 = 16

log₂₅₆16 = 1/2

400

Rewrite in log form:

(1/6)³ = (1/216)

log_(1/6)(1/216) = 3

500

Rewrite in log form:

64^-1/2 = 1/8

log₆₄(1/8) = -1/2

Log to Exponent

100

Rewrite in exponential form:

log₂4 = 2

2² = 4

200

Rewrite in exponential form:

log₈64 = 2

8² = 64

300

Rewrite in exponential form:

log₅(1/25) = -2

5^-2 = 1/25

400

Rewrite in exponential form:

log_(1/8)64 = -2

(1/8)^-2 = 64

500

Rewrite in exponential form:

log100 = 2

10² = 100

Condense & Expand Logs

100

Expand:  log 35x

log 35 + log x

200

Condense: log 2 + log 9

log 18

300

Expand: log 7x²

log 7 + 2 log x

400

Condense: 4 log 2 + 3 log x

log 16x³

500

Condense:  2 log 3 - 2 log 5

log (9/25)

Log Equations

100

Solve for x. 

Log(2x + 4)= Log(3x-8)

x = 12

200

Solve for x.

Ln(2x+1) = Ln(11)

x = 5

300

Solve for x.

Log_2(x+4)=5

x=28

400

log₂x-log₂10 = 2

x = 40

500

2log₅4+log₅x = 3

125/16 OR 7.8125