Exponentials And Logarithms

Solve the Basic Logarithm

100

Find x

Log_2 16=x

X=4

200

Solve For X

log_3 27=x+2

X=1

300

Solve For X

log_4 1=x

X=0

400

Solve For X

log_5 (1/25)=x

X = -2

500

Solve for X

log_2 (1/4)=2x

x=-1

600

Solve for x.

log_2 (-1)=x-4

x=log_2(y-1)+4

Convert To A Logarithm

100

Convert to a Logarithm of form

log_b x=y

2^3=8

log_2 8=3

200

Convert to a Logarithm of form

log_b x=y

12^3=1728

log_12 1728=3

300

Convert to a Logarithm of form

log_b x=y

3^0=1

log_3 1=0

400

Convert to a Logarithm of form

log_b x=y

10^(x+2)=29

log 29=x+2

500

Convert to a Logarithm of form

log_b x=y

5^3=x-3

log_5 (x-3)=3

600

Convert to a logarithmic form

log_b x=y

3^(x+1)=0.5

x+1=log_3 (0.5)

Convert To An Exponential

100

Convert the following to an exponential equation.

log_2 32=5

2^5=32

200

Convert the following to an exponential equation.

log_2 x=y

x=2^y

300

Convert the following to an exponential equation.

ln 1=0

e⁰ = 1

400

Convert the following to an exponential equation.

log_2 (x+3)=8

2^8=x+3

500

Convert the following to an exponential equation.

log_7 4=x-6

7^(x-6)=4

600

Convert the following to an exponential equation.

log(x+1)=4

x+1=10^4

Expand or Compress

100

Expand the following Logarithm.

log((x^3y^4)/z^6)

3logx+4logy-6logz

200

Compress the following logarithm.

log_3 5+5log_3 2

log_3 160

300

Rewrite the following logarithm

log(a+b)+log(a-b)-2logc

log((a^2-b^2)/c^2)

400

Expand the following logarithm using the power and quotient rules.

log((3x^2)/(x+1)^10)

log(3x^2)-10log(x+1)

500

Compress the following logarithm using the power and product rules.

log5+2logx+3log(x^2+5)

log((5x^2)/(x^2+5)^3)

600

Expand the following logarithm using the power and product rules.

log(x^4y^3z^5)

4logx+3logy+5logz

Solve For X

100

Solve For X

3^x=81

x=4

200

Solve for X

2^x=16^4

x=16

300

4^(x+2)=2^6

x=1

400

Solve for X. 

5^x=24

x=1.97

500

Solve for X.

2^(x+4)=7

-1.19

600

Solve for x.

25=5^(-x+1)

x=-1