Solving Logs Flashcardizz

Front

What is a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(a), b is the base.

Front

Evaluate log_9(81).

Back

2, because 9^2 = 81.

Front

How do you solve for x in the equation 5^(2x-6) = 625?

Back

x = 5, because 625 = 5^4 and 2x - 6 = 4.

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: (1/2)^(x-3) = 16^(3x+1).

Back

x = -1/13.

Front

Evaluate log_8(4).

Back

2/3, because 8^(2/3) = 4.

Front

What does log(x+6) = 1 mean?

Back

It means x + 6 = 10^1, so x = 4.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation.

Front

If log_b(a) = c, what is a in terms of b and c?

Back

a = b^c.