Exponentials And Logarithms

Misc

100

Find x

2^x=16

X=4

200

Solve For X

3^(x+2)=27

X=1

300

Solve For X

4^x=1

X=0

400

True or False

x=(log 55)/(log 7)  can  be  used

to  solve  7^x=55

True

500

Mohal is going to invest $830 and leave it in an account for 8 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Mohal to end up with $1,110?

3.63%

600

Solve for x.

ln(x^2)=ln(-4x+12)

x=-6  and  x=2

Log/Exponential Conversion

100

Convert to a Logarithm of form

log_b x=y

2^3=8

log_2 8=3

200

Convert the following to an exponential equation.

log_8 1=0

8⁰ = 1

300

Convert to a Logarithm of form

log_b x=y

2^(x+2)=29

log_2 29=x+2

400

Convert to a Logarithm of form

log_b x=y

5^3=x-3

log_5 (x-3)=3

500

Convert the following to an exponential equation.

log((x)/(x+1))=4

(x)/(x+1)=10^4

600

Convert to a logarithmic form

log_b x=y

3^(x+1)=0.5

x+1=log_3 (0.5)

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

Condense the following logarithm

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

log((a^2+ab)/c^2)

400

Expand the following logarithm using the power and quotient rules.

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

2log(3)+2log(x)-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)/(w^2))

4logx+3logy+5logz-2logw

Solve For X

100

Solve For X

log_4(16)=x

x=2

200

Solve for X

log_2(x)=4

x=16

300

log_x(25)=2

x=5, -5

400

Solve for X. 

log(x)+log(5)=30

x=(10^30)/5

500

Solve for X.

log(x)+log(x-2)=log(35)

x= 7

600

Solve for x.

ln(x)-ln(x-1)=2

x=(-e^2)/(1-e^2)