The Math Way

1

100

Log₂x=-4

Write in exponential form.

2^-4=x

200

4=log₇2401

What is the equivalent exponential form of the equation?

7⁴=2401

300

₁₀log23

Evaluate the expression without using a calculator.

23

400

log₄(x-5)=2

Write the equation in its equivalent exponential form.

4²=x-5

500

7^-1.4

^{Approximate the following number using a calculator.}

0.066

2

100

2^x=29

What is the solution in terms of natural logarithms?

ln29/ln2

200

6^2x-8=1296

Solve for x.

6

300

log10⁷

^{Evaluate or simplify the expression without using a calculator.}

7

400

2⁴=16

Write the equation in its equivalent logarithmic form.

log₂16=4

500

8²=64

Write the equation in its equivalent logarithmic form.

2=log₈64

3

100

log₂x=-5

Write the equation in its equivalent exponential form.

2^-5=x

200

log₁₁121

Find the exact value of the logarithm without using a calculator.

2

300

3^3x-22=9

Solve for x.

8

400

log50+log2

Where possible, evaluate logarithmic expressions.

2

500

16^x=32

Solve the exponential equation by expressing each side as a power of the same base and then equating exponents.

5/4

4

100

log₅x=3

Solve the following logarithmic equation.

125

200

log₂(x+16)=4

Solve the following logarithmic equation.

0

300

log₁₂16

Use common logarithms or natural logarithms and a calculator to evaluate the expression.ROUND TO FOUR DECIMAL PLACES.

1.1158 

400

ln x=4

What is the solution in terms of e.

e⁴

500

9^x+8=81^x-7

^{Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.}

22

5

100

7^x=29

What is the solution in terms of natural logarithms?

ln 29/ ln 7

200

log_b(z²x)

Use properties of logarithms to expand each logarithmic expression as much as possible.  Evaluate logarithmic expressions without using a calculator if possible.

2log_bz+log_bx

300

log₇(343x)

Use properties of logarithms to expand the logarithmic expression as much as possible.  Where possible, evaluate logarithmic expressions without using a calculator.

3+log₇x

400

8^x=32

Solve the exponential equation by expressing each side as a power of the same base and then equating exponents.

5/3

500

log₃x=4

Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer.  

81