Logarithmic Equations

Front

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

Back

10^(y+2)=x

Front

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

Back

log(100)=x+5

Front

What is the exponential form of f(x) = log₃(x)?

Back

f(x) = 3^x

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another 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

What is the product rule for logarithms?

Back

log_b(mn) = log_b(m) + log_b(n) for any positive m and n.

Front

What is the quotient rule for logarithms?

Back

log_b(m/n) = log_b(m) - log_b(n) for any positive m and n.

Front

What is the power rule for logarithms?

Back

log_b(m^p) = p * log_b(m) for any positive m and real number p.

Front

Solve for x: log_10(x) = 3.

Back

x = 10^3 = 1000.

Front

Solve for x: 2^(x-1) = 8.

Back

x - 1 = 3, so x = 4.