exponential & logarithmic Forms
log_5 (125) = 3
5^3 =125
log_10 (1000) = 3
10^3 =1000
condense log(a) + log(b) into a single logarithm.
log(ab)
solve for x: 2^x = 8
x=3
How many years will it take for an initial investment of $5000 to grow to $7000 if it is invested at a 5% interest rate, compounded annually?
It will take approximately 7 years (rounding up to the nearest full year for the investment to reach at least $7000)
2^x = 32
log_(32)=x
log_2 (x) = 5
log 2^5 =x
condense log(x) - log(y) into a single logarithm
log(x/y)
solve for x: log _10 (x)= 2
x=100
How many years will it take for an initial investment of $5000 to grow to $7000 if it is invested at a 5% interest rate, compounded annually?
The San Francisco earthquake was 1000 times more intense than the recent earthquake.
log_10 (1/1000) = -3
10^-3 = 1/1000
log_5 (25) =2
5^2 = 25
condense 3 * log(m) into a single logarithm.
log(m^3)
solve for x: 3^(x+1)=27
x = 2
apple juice has a hydrogen ion concentration f [H^+] =0.0003 moles per liter. what is the pH level? is it acidic or basic?
e^4 = y
in y =4
log_3 (1) = 0
3^0= 1
condense (1/2) * log(n) into a single logarithm.
log n^(1/2)
solve for x: log_2 (16)= x
x=4
pH=-log10[H+], where [H+]=0.0001
pH=-log10(0.0001)=4
8^2/3 = 4
log _8 (4) = 2/3
log_ 4 (64) = y
4^y = 64
condense log(x) + log (y) into a single logarithm.
log (xy)
solve for x: 10^(2x)=1000
P=200*10^(k*t), with P=800, P(0)=200, t=4.
k=0.1505