Solving log equations

Front

Rewrite 3^4 = 81 in logarithmic form.

Back

log_3 81 = 4

Front

If log_3(n^2 + 4n) = log_3(35 + 2n), what are the possible values of n?

Back

5, -7

Front

Solve the equation log(9 - x) = log(2x - 6). What is x?

Back

5

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

What is the product rule of logarithms?

Back

log_b (xy) = log_b x + log_b y.

Front

What is the quotient rule of logarithms?

Back

log_b (x/y) = log_b x - log_b y.

Front

What is the power rule of logarithms?

Back

log_b (x^p) = p * log_b x.

Front

Solve for x: -10log_2 x + 8 = -12. What is x?

Back

4

Front

What is the definition of the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.718.