Converting Logarithms and Exponentials

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

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If a^b = c, then log_a(c) = b.

Front

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

Back

ln(9) = x.

Front

Write the logarithmic form of 9^2 = 81.

Back

log_9(81) = 2.

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is e, approximately equal to 2.718.

Front

How do you convert log_a(b) to exponential form?

Back

If log_a(b) = c, then a^c = b.

Front

What is the change of base formula for logarithms?

Back

log_a(b) = log_c(b) / log_c(a), where c is any positive number.

Front

Convert log_2(16) to exponential form.

Back

2^4 = 16.

Front

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

Back

x = 2, because 10^2 = 100.

Front

What is the definition of the common logarithm?

Back

The common logarithm is the logarithm with base 10, denoted as log(x) or log_10(x).