Exponential and Logarithmic Expressions

Front

What is the base of the exponential expression when rewriting 8 = 2^(5x + 7)?

Back

2

Front

Evaluate the logarithmic expression: log_7(49)

Back

2

Front

Write the expression (√5b)^{3} in exponential form.

Back

(5b)^{(3/2)}

Front

Rewrite the equation 9^2 = 81 in logarithmic form.

Back

log_9(81) = 2

Front

Evaluate the expression: log_2(8)

Back

3

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

Front

Convert the exponential equation 2^x = 16 to logarithmic form.

Back

log_2(16) = x

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any base k.

Front

If log_10(100) = x, what is the value of x?

Back

2

Front

What is the relationship between exponential and logarithmic functions?

Back

They are inverse functions; if y = b^x, then x = log_b(y).