math

graphing exponential func.

plug in usable terms find asymptote: k-value domain: all real numbers range: k-value to (-)infinity j curve

graphing logarithmic func.

inverse of exponential so swap coords plug in usable terms asymptote mirrors inverse k-value domain: inverse k-value to (-)infinity range: all real numbers

answer in the form of a, b, and c: log((x^2*y^2)/z^3)

separate logs by taking exponent and putting it in front then multiplication is addition and division is subtraction substitute log(x) as a, log(y) as b, and log(z) as c

solve: log2(x) + log2(x+1) = log2(6)

combine first two terms and drop logs solve and factor quadratic from there

solve: log9(81)+log9(1/9)+log9(3) = log(x)

combine first 3 terms and drop logs

solve: log4(x+14)-log2(x)=1

change log4(x+14) to log2(x+14)/log2(4) combine x's and evaluate log2(4) and combine with one circle of logs and solve

solve: log2(x) = log4(x+6)

change base of log4(x+6) to log2(x+6)/log2(4) subtract log2(x+6) over and combine with log2(x) solve log2(4) and circle of logs

solve: ln(x)+1/ln(x)=2

substitute ln(x) as y factor new equation find y set y equal to ln(x) and solve for x

solve: 2ln(x)^2 = 3ln(x)-1

substitute ln(x) as y factor new equation find y set y equal to ln(x) and solve for x

solve: 3^(x+1) = 15

change to get like bases drop bases solve

solve and give answers in form of a + log(b): 2(10^(x+1)) = 15

divide by 2 log both sides x+1log(10) cancels to x+1 subtract 1 to the other side answer complete

solve and give answer in form of ln(a)/ln(b): 6^x = 3^(x+2)

ln both sides separate x+2ln(3) to xln(3)+2ln(3) subtract xln(3) to the other side undistribute the x into the ln(6) and ln(3) to make x(ln(6)-ln(3)) divide by (ln(6)-ln(3)) get x = 2ln(3)/(ln(6)-ln(3)) simplify to ln(9)/ln(2)

solve and give answer in form of ln(a)/ln(b): 6^x-1 = 3^x+2

ln both sides separate x-1ln(6) to xln(6)-1ln(6) separate x+2ln(3) to xln(3)+2ln(3) subtract xln(3) to other side add 1ln(6) to other side undistribute x to get x(ln(6)-ln(3))=1ln(6)+2ln(3) divide by (ln(6)-ln(3)) get x = 1ln(6)+2ln(3)/(ln6)-ln(3)) simplify to ln(54)/ln(2)

solve: 4^x-9*2^x+8

subtitute 2^x as y convert 4^x to 2^2x because math write new equation: y^2-9y+8 factor and solve for y set y equal to 2^x and solve for x

solve: solve: 3^(2x+2)+8*3^(x+1)=9

substitute 3^x as y get 9y^2+24y-9=0 factor and solve quadratic set y = to 3^x and solve for x

graph e^(x-3)+2

find easy terms to put in and find ordered pairs: (3,3) (4, e+2) asymptote at y=2 domain: all real numbers range 2 to infinity

find/graph inverse of e^(x-3)+2

swap x and y and solve for y get y=ln(x-2)+3 swap ordered pairs from original reflect over y=x asymptote at x=2 domain: 2 to infinity range: all real numbers

group of leopards growth is modeled by N = 10e^(0.4t)

how many leopards after 2 years

how long until 100 leopards

how long until leopards double

first, plug in 2 for t and solve

second, set N = 100 and solve or calc it for this divide by 10 then ln both sides and divide by 0.4

third, set N = 20 and solve or calc it for this divide by 10 then ln both sides and divide by 0.4

use FV = PV(1 + r/(100*n)^(nt)

invested 100

a: if interest compounded annually at 5%, write expression and find after 20 yrs

b: if interest compunted monthly at 5/12%, and this exceeds the answer to last problem in m months, write inequality and find m

first use formula: FV=PV(1+r/(100*n)^(nt)

a: first FV = 100(1.05)^t second: plug in 20 for t

b: first set 256<100(1+(5/12)/(1200))^(12t) second: find t