Exponential to Logarithmic Flashcard

Front

Write b^k = m into logarithmic form.

Back

log _b m = k

Front

A population of bacteria doubles every 3 hours. If there are 100 bacteria initially, how many will there be after 12 hours?

Back

1600

Front

What is the transformation of the function f(x) = 2^(x+1) - 2?

Back

Vertical Translation down 2 and Horizontal Translation left 1

Front

Find the value of x in the equation 4^x = 64 using logarithms.

Back

3

Front

Solve the equation 2^x = 16 using logarithms.

Back

x = 4

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

Convert the logarithmic equation log₁₀ 100 = 2 into exponential form.

Back

10² = 100

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

If log₂ 8 = x, what is the value of x?

Back

x = 3

Front

What is the product rule for logarithms?

Back

log_b (xy) = log_b x + log_b y