Exponents and Logarithms

Log <-> Exp

100

log₄16=2

4²=16

200

log x = 7

10⁷ = x

300

3^x = 81

log₃81 = x

400

ln 23 = x

e^x = 23

500

log_x y = z

x^z = y

Logarithms

100

A logarithmic operation is the inverse of this operation.

What is exponential?

200

Logarithms with base e are called:

Natural Logarithms

300

Write the product rule for logarithms.

What is log m + log n = log mn?

400

The log of 1, regardless of the base, is this.

What is 0?

500

Write the power rule for logarithms.

alog_bx = log_bx^a

Expand

100

Expand log(5x)

What is log 5 + log x?

200

Expand ln(x²y⁵).

What is 2lnx + 5lny

300

Expand log((3xyz)/4)

What is log 3 + log x + log y + log z - log 4?

400

Expand ln(3x²*z³/5x).

What is ln 3 + 2lnx + 3lnz - (ln 5 + ln x)?

500

Expand log(x²y⁸z⁴)^1/2

What is (log x + 4log y + 2log z)?

Condense

100

Condense log 7 + log b

What is log 7b?

200

Condense 4log 2 + 3log 4

What is log 1024?

300

Condense ln x + ln 3 + 2ln y -ln e

What is ln(3xy²)-1?

400

Condense 1/3logx - 2/3log y

What is log (x/y²)^(1/3)?

500

Condense 1/2(3log x + 3log y - 7log z).

log(x^3/2y^3/2/z^7/2) = log (x³y³/z⁷)^1/2