Math Log and E rules

When given values and an equation tl plug knto

-expand given completely -make sure values given are present in expanded equation -plug in values -solve

When the rquation has the same log or ln

-simplify/condense COMPLETELY -take away log/ln -solve

ln1

0

logb of 1

0

Logb of b

1

lne

1

e

2.72

Decreasing/increasing exponential function

A(t)=a(1+/-r)^t

How to find a function's equation using two points **

A) set up a system of equations using exponential equations B) divide two equations to eliminate a value and solve for b C) plug b value into an og. Equation to fimd a value D) rewrite functions equation using values found for a and b

Compound interest formula

A=P(1+r/n)^nt

Compound continuously formula

A=Pe^rt

Variable in the exponent

Find common base, if bases are different, see if you can make the larger one a power of the smaller one.

When 0<b<1

Graph is decreasing

When b>1

Graph is increasing

Solving exponential equations using a common base

If they do not have a common base, tale the log! -isolate the variable -able to take "log" because the log have the same value -exponents go before log -can use this with natural log***

Horizontal asymptotes

Occur usually at lowest point of graph

How to find y intercept if vert shifts

Plug in 0 for x

Fractional base and variable exponent

Use a negative exponent when rewriting with the common base

Log b of b^x

X

b^logb of x

X

e^knx

X

lne^x

X

"A" value in exponential function

Y-intercept, when no additional vert shifts

Standard form of an exponential function

Y=a(b)^x

Logarithm

Y=log base 2 of x, 2^y=x