Exponential and Log Equations

Front

Solve for x: 2^(3x + 1) = 32

Back

x = 4/3

Front

Expand: 2log_3(6) + 2log_3(x)

Back

2log_3(6) + 2log_3(x)

Front

Write as a single log: log 12 + 2 log x

Back

log(12x^2)

Front

Solve: 9^(8-x) = 27^(x-3)

Back

x = 5

Front

Expand log_6(5x^3/y)

Back

log_6(5) + 3log_6(x) - log_6(y)

Front

Definition: Exponential Function

Back

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

Front

Definition: Logarithm

Back

The inverse operation to exponentiation, log_b(a) is the exponent to which b must be raised to yield a.

Front

Change of Base Formula

Back

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

Front

Definition: Properties of Logarithms

Back

1. log_b(mn) = log_b(m) + log_b(n) 2. log_b(m/n) = log_b(m) - log_b(n) 3. log_b(m^p) = p * log_b(m)

Front

Solve for x: 3^(2x) = 81

Back

x = 2