Solving Log Equations (No Properties Required)

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

How do you rewrite log_7(729) using the change of base rule?

Back

log_7(729) = log(729) / log(7) using the change of base formula.

Front

How do you rewrite log_5(75) using the change of base rule?

Back

log_5(75) = log(75) / log(5) using the change of base formula.

Front

If log_11(b) = 3, what is the value of b?

Back

b = 11^3 = 1331.

Front

What is the value of log_2(16)?

Back

log_2(16) = 4, because 2^4 = 16.

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 relationship between logarithms and exponents?

Back

If b^y = x, then log_b(x) = y.

Front

How can you solve the equation -10log_2(x) + 8 = -12 for x?

Back

First, isolate the logarithm: -10log_2(x) = -20, then log_2(x) = 2, so x = 2^2 = 4.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a certain value.

Front

What is log_10 commonly referred to as?

Back

log_10 is commonly referred to as the common logarithm.