Solving Exponential & Logarithm Equations

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, 2^x = 8.

Front

How do you convert an exponential equation to logarithmic form?

Back

To convert an exponential equation a^b = c to logarithmic form, use log_a(c) = b.

Front

What is the logarithmic form of 5^3 = 125?

Back

log_5(125) = 3.

Front

What is the property of logarithms that allows you to expand log(a*b)?

Back

log(a*b) = log(a) + log(b).

Front

What is the property of logarithms that allows you to condense log(a) - log(b)?

Back

log(a) - log(b) = log(a/b).

Front

How do you solve the equation 3^(-3r) = 3^5?

Back

Set the exponents equal: -3r = 5, then r = -5/3.

Front

What is the value of log_10(1000)?

Back

log_10(1000) = 3, because 10^3 = 1000.

Front

What is the change of base formula for logarithms?

Back

log_a(b) = log_c(b) / log_c(a) for any base c.

Front

What is the value of log_2(8)?

Back

log_2(8) = 3, because 2^3 = 8.

Front

What does it mean to condense logarithmic expressions?

Back

Condensing logarithmic expressions means to combine multiple logs into a single log using properties of logarithms.