HPC Unit 6: Exponential and Logarithmic Equations

Front

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

Back

log_6(216) = 3

Front

What is log_5(125)?

Back

3

Front

Convert log(x) = y + 2 to exponential form.

Back

10^(y + 2) = x

Front

Solve for x: (-6) * 15^(x + 9) = -150

Back

-7.81

Front

Solve for x: log_5(4x - 7) = log_5(x + 5)

Back

4

Front

Define an exponential function.

Back

A function of the form f(x) = a * b^x, where a is a constant, b > 0, and b ≠ 1.

Front

What is the base of a logarithm?

Back

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

Front

Convert the logarithmic equation log_b(a) = c to exponential form.

Back

b^c = a

Front

What is the inverse relationship between exponential and logarithmic functions?

Back

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

Front

What is the change of base formula for logarithms?

Back

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