Converting Logarithms

Front

Rewrite e^x = 9 using a logarithm

Back

ln 9 = x

Front

Write in exponential form: log_2 32 = 5

Back

2^5 = 32

Front

Write in logarithmic form: 2^-1 = 0.5

Back

log_2 0.5 = -1

Front

Write in exponential form: log_2(1/8) = -3

Back

2^-3 = 1/8

Front

Write in exponential form: log_36 1 = 0

Back

36^0 = 1

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 logarithmic equation log_b a = c to exponential form.

Back

b^c = a

Front

What is the base of a natural logarithm?

Back

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

Front

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

Back

x = 2, because 10^2 = 100.

Front

What is the change of base formula for logarithms?

Back

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