Converting Logarithms and Exponentials

Front

What is the relationship between logarithmic and exponential forms?

Back

If b^y = x, then log_b(x) = y.

Front

Convert the exponential equation e^x = 9 to logarithmic form.

Back

ln(9) = x.

Front

Write the logarithmic form of the equation 9^2 = 81.

Back

log_9(81) = 2.

Front

Convert the logarithmic equation log_2(32) = 5 to exponential form.

Back

2^5 = 32.

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number.

Front

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x.

Front

What is the base of a natural logarithm?

Back

The base of a natural logarithm is e (approximately 2.718).

Front

Convert log_10(100) to exponential form.

Back

10^2 = 100.

Front

What is the value of log_2(8)?

Back

3, because 2^3 = 8.

Front

How do you express log_5(25) in terms of exponents?

Back

log_5(25) = 2, because 5^2 = 25.