Solve exponential & logs

Front

What is the definition of an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the logarithmic form of the equation 2^3 = 8?

Back

log_2(8) = 3

Front

How do you solve the exponential equation 14e^(3x+2) = 560?

Back

1. Divide both sides by 14. 2. Take the natural logarithm of both sides. 3. Solve for x.

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time in years.

Front

What is the definition of a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number.

Front

Rewrite the equation 5^2 = 25 in logarithmic form.

Back

log_5(25) = 2

Front

What is the growth model for exponential growth?

Back

y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

How do you convert from exponential form to logarithmic form?

Back

If a^b = c, then log_a(c) = b.

Front

What is the value of log_10(1000)?

Back

3, because 10^3 = 1000.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions grow rapidly, while logarithmic functions grow slowly; they are inverses of each other.