Need math help with logarithmic functions!

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Which of the following equations shows the logarithmic equation below in exponential form?

$\log_{3} 81 = 4$

b. $3 to the power of 4 equals 81$

c. $4 to the power of 81 equals 3$

d. $81 cubed equals 4$

Which of the following equations shows the logarithmic equation below in exponential form?

$\log_{36} (\frac{1}{6}) = - \frac{1}{2}$

b. $36 to the power of left parenthesis negative bevelled 1 half right parenthesis end exponent equals bevelled 1 over 6$

c. $6 to the power of left parenthesis negative bevelled 1 half right parenthesis end exponent equals space 36$

d. $left parenthesis bevelled 1 over 6 right parenthesis to the power of left parenthesis bevelled fraction numerator negative 1 over denominator 2 end fraction right parenthesis end exponent equals 36$

Which of the following logarithms is equal to 1?

a. $log subscript 8 1$

b. $log subscript 1 1$

c. $log subscript 9 9$

d. $log subscript 2 8$

Evaluate the logarithm $\log_{4} (\frac{1}{2})$

b. Log x

c. log 2

d. x

Find the inverse of the function y = $\log_{7} 49^{x}$

b. y=2x

c. $y equals 7 to the power of x$

d. y=7x

What is the domain and range of the graph of the function below?

y = log (x-2)

a. Domain: all real numbers; Range: y > 2

b. Domain: all real numbers; Range: y < 2

c. Domain: x > 2; Range: all real numbers

d. Domain: x < 2; Range: all real numbers

Which of the following shows the graph of the function below?

$y = \log_{5} (x + 4)$

The Richter scale is used for measuring the magnitude of an earthquake. The Richter magnitude R is given by the model below, where E is the energy (in kilowatt-hours) released by the earthquake.

R = 0.67 log (0.37E) + 1.46

Suppose an earthquake releases 14,500,000,000 kilowatt-hours of energy. What is the earthquake’s magnitude? Round to three decimal places.

a. 4.400

b. 3.979

c. 8.268

d. 7.979

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