M4U4D2 Skillcheck Exponents and Logarithms Basics

Front

Write the exponential equation as a logarithm: 6^3 = 216

Back

log_6(216) = 3

Front

Convert 10^(x+5) = 100 to logarithmic form.

Back

log(100) = x + 5

Front

Change to Logarithmic Form: 12^2 = 144

Back

log_12(144) = 2

Front

Rewrite log_2(8) = 3 in exponential form.

Back

2^3 = 8

Front

Change to Logarithmic Form: 2^6 = 64

Back

log_2(64) = 6

Front

Definition of a logarithm: If a^b = c, then log_a(c) = b.

Back

This defines the relationship between exponents and logarithms.

Front

What is the base of a logarithm?

Back

The base is the number that is raised to a power to obtain a given number.

Front

Convert the logarithmic equation log_10(1000) = 3 to exponential form.

Back

10^3 = 1000

Front

What is the change of base formula for logarithms?

Back

log_a(b) = log_c(b) / log_c(a) for any base c.

Front

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

Back

b^y = x