Solving Logarithmic Equations

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

What is the base of the common logarithm?

Back

10

Front

What is the relationship between logarithmic functions and exponential functions?

Back

Logarithmic functions are the inverse of exponential functions.

Front

Solve the equation: log₂(x²-6) = log₂(2x+2)

Back

4

Front

Solve the equation: log₈(4x+4) = 2

Back

15

Front

What is the change of base formula for logarithms?

Back

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

Front

What is the product rule of logarithms?

Back

log_b(xy) = log_b(x) + log_b(y) for any positive x and y.

Front

What is the quotient rule of logarithms?

Back

log_b(x/y) = log_b(x) - log_b(y) for any positive x and y.

Front

What is the power rule of logarithms?

Back

log_b(xⁿ) = n * log_b(x) for any positive x and n.

Front

What is the value of log₁₀(100)?

Back

2