Solving Logarithmic Equations

Front

Solve for x: log₂(2) + log₂(8x) = 6

Back

x = 4

Front

log₉(10) - log₉(x-3) = log₉(72)

Back

x = 113/36

Front

Solve for x: log₅(4x-7) = log₅( x + 5)

Back

x = 4

Front

What is the base of the common logarithm?

Back

10

Front

Solve for x: log₂(x + 3) = 4

Back

x = 13

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 change of base formula for logarithms?

Back

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

Front

Solve for x: log₃(27) = x

Back

x = 3

Front

What is the product rule of logarithms?

Back

log_b(MN) = log_b(M) + log_b(N) for any positive M and N.

Front

What is the quotient rule of logarithms?

Back

log_b(M/N) = log_b(M) - log_b(N) for any positive M and N.