Exponential to Logarithmic

Front

What is the relationship between exponential and logarithmic functions?

Back

Logarithmic functions are the inverses of exponential functions. If b^k = m, then log_b(m) = k.

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, log_b(m) = k means b^k = m.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(m), b is the base.

Front

What is the value of log_10(1)?

Back

log_10(1) = 0 because 10^0 = 1.

Front

What is the value of log_b(b)?

Back

log_b(b) = 1 because b^1 = b.

Front

What is the value of log_b(1)?

Back

log_b(1) = 0 because b^0 = 1.

Front

If 4^x = 64, what is x?

Back

x = 3 because 4^3 = 64.

Front

If log_2(8) = x, what is x?

Back

x = 3 because 2^3 = 8.

Front

What is the change of base formula for logarithms?

Back

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

Front

If 5^y = 25, what is y?

Back

y = 2 because 5^2 = 25.