Chapter 6 review

Inverse Property of Logarithms and Exponents

10^(log x) = x

Write this equation in exponential form: log8 64 = 2

8^2 = 64

Find an if a1 = 4, r = 3, n = 7

a7 = 2916

nth Term of a Geometric Sequence

an = a1(r)^(n-1)

The Property of Equality for Exponential Functions

b^x = b^y if and only if x = y

Inverse Property of Base e and Natural Logarithms

ln e^x = x e^(ln x) = x

Power Property of Logarithms

log a^b = b log a

Product/Quotient Property of Logarithms

log ab = log a + log b log a/b = log a - log b

Write this equation in logarithmic form: 7^3 = 343

log7 343 = 3

Property of Equality for Logarithmic Functions

logb x = logb y if x = y

Solve for x: e^(3x+2) - 2 = 16

x = ((ln 18) - 2)/3 or x = ~0.2968

Solve for x: 3^(x-3) = 16

x = (log 16/log 3) + 3 or x = ~5.5237

Solve for x: 27^x = 3^(x+2)

x = 1

Solve for x: 2 log 3 + log 5x = log 10 - log 2

x = 1/9

Solve for x: log5 (2x+3) = 2

x = 11

Solve for x: ln (x-1) + 5 = 7

x = e^2 + 1 or x = ~8.3891

The Exponential Growth Function

y = ab^(x-h) + k

Exponential Growth/Decay

y=ae^kt y=ae^-kt

A field of rice yields 20% more rice each year. How many years will it take to double the amount of rice yielded?

~3.5 years