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Exponential and Logarithms

100

2³=x

x=8

200

6^x=216

x=3

300

log₄(256)=x

x=4

400

Convert to exponential

log₇(2x)=13

7¹³=2x

500

Solve for x.

log₅(3x+5)=log₅(8x+3)

x=0.4

Product Rule

100

Condense:

log₃(5)+log₃(6)

log₃(30)

200

Condense:

log₁₁(7)+log₁₁(x)

log₁₁(7x)

300

Condense:

log₃(4y)+log₃(y+4)

log₃(4y(y+4))

400

Solve:

log₄(6x)+log₄(10x)=log₄(240)

x=2

500

Solve:

log₂(y)+log₂(y-3)=2

y=4

Quotient Rule

100

Condense:

log₃(15)-log₃(5)

log₃(3)

200

Condense:

log₁₆(27x)-log₁₆(3x)

log₁₆(9)

300

Condense:

log₂(x-5)-log₂(3x+1)

log₂((x-5)/(3x+1))

400

Solve:

log₂(4x+8)-log₂(2)=4

x=3

500

Solve:

log₂(4m+28)-log₂(5m+35)=log₂(1/m)

m=5/4

Power Rule

100

Condense:

4log₃(2)

log₃(16)

200

Condense:

2log₃(4x)

log₃(16x²)

300

Solve:

2log₇(b)=log₇(49)

b=7

400

Solve:

5log₃(a)=log₃(63)

a=2.29

500

Solve:

log₂(4^x)=log₂(32)

x=2.5

Mixed

100

Given log_m(3)~0.23 and log_m(8)~0.57

Evaluate log_m(24)

0.80

200

Given log_y(4)~0.283 and log_y(5)~0.563

Evaluate log_y(5/4)

0.28

300

Given log_f(12)~1.277 and log_f(2)~0.356

Evaluate log_f(24)*log_f(6)

1.504

400

Solve:

log(x)-log(6)=2log(4)

96

500

Solve:

2log₄(x)-log₄(x-1)=1

x=2