Converting Log and Exponential Form
Convert to Exponential Form:
log_2(8)=x
2^x=8
Solve for x:
log_3(x-3)=log_3(55)
x=58
Condense the Logarithms:
log_3(2x)-log_3(5y)
log_3((2x)/(5y))
Solve using Logarithms. Round the answer to the hundredth if necessary:
6^x=90
x=2.51
June made an initial deposit of $5700 in an account for her son. Assuming an interest rate of 6% compounded
quarterly, how much will the account be worth in 15 years?
$13,926.35
Convert to Logarithmic Form:
4^y=x
log_4(x)=y
Solve for x:
log_5(x+6)=log_5(3x)
x=3
Completely Expand the Logarithm:
log((2x)/y)
log(2)+log(x)-log(y)
Solve Using Logarithms. Round the answer to the hundredth if necessary:
3^(7x)=108
x=0.61
If Bob deposits $5000 at the end of each year for 15 years in an account paying 6% interest compounded
annually, find the amount he will have on deposit.
$116,379.85
Convert to Exponential Form:
log_(x-1)(4)=2y
(x-1)^(2y)=4
Solve for x:
2ln(2)+ln(x)=ln(x+12)
x=4
Condense the Logarithms:
2ln(3)-2ln(x)+4ln(y)
ln((9y^4)/x^2)
Solve by Converting:
log_4(x)=5
x=1024
In order to purchase a home, a family borrows $45,000 at an annual interest rate of 13%, to be paid back over a 30-year period in equal monthly payments. What is their monthly payment?
$497.79