Solving Logs
Solve 62x+3=613
x=5
Expand
log 36
log 3 + log 12
log 4 + log 9
log 2 + log 18
log 6 + log 6
Change the form
log4 256 = 4
44 = 256
Simplify
ln(e3.4)
3.4
Tell if the following is linear or exponential:
A scientist notices that a worm triples in length every month.
log (5d-5) = log 15
d=4
log x - log 41
log x/41
Change the form
73 = 343
log7 343 = 3
Solve for x
e4x-8 = 10
ln(10) + 8
________
4
Tell if it is linear or exponential
A dog eats two cups of food every day.
Linear
log (6h - 10) = log (4h + 32)
h = 21
Expand into an expression with three terms.
log 12x
log 4 + log 3 + log x
log 6 + log 2 + log x
Change the form
log3 81 = 4
34 = 81
Solve for x
ln(3x-2) = 5
e5+2
______
3
Write an equation to model the situation
A scientist is working in a lab with the flu virus. He notices that the virus has cells that triple every hour. The scientist starts with ten cells.
f(x) = 10 * 3x
log5(4x-5) = 3
x=32.5
Expand
log x5
5 log x
Change the form
log 1000 = 3
Condense
ln(4) + ln (2) + ln (y)
ln (8y)
Write an equation to model the situation then find how much money will be in the account in 5 years.
A bank increases your money by 1.5 times for every year you do not take money out of the account. You put $25 in the account.
f(x) = 25 * 1.5x
$189.84
43x-2=256
x=2
Condense
12 log f
log f12
Change the form
x2 = 25
logx 25 = 2
Expand
ln(2/5)
ln(2) - ln(5)
Write an equation to model the situation then find the lamp's worth after 3 years.
You buy an antique lamp for $30. The value goes up by 1.25 each year you have it.
f(x) = 30 * (1.25)x
$58.59