Properties of Logs

At what rate compounded continuously will $13,575 have to be invested for the amount to reach $21.478 in 5 years?

$21.478=13575(e)r(5)$21.478=13575(e)r(5) 21.47813575=in(e)r(5)21.47813575=in(e)r(5) in (2147813575)5=rin (2147813575)5=r in (2147813575)5=0.091100=9.17in (2147813575)5=0.091100=9.17

Rewrite the exponential function of 132=169132=169 as a Logarithmic Function.

132=169 Base:13 Exponetnt=2 argument=169 132=169 Base:13 Exponetnt=2 argument=169 log13(169)=2 log13⁡169=2

Expand the following: logAC=logbAC−1log⁡AC=logb⁡AC−1

=logb(A)+logb(C−1)=logb⁡(A)+logb⁡(C−1) =logbA+(−1)logbC=logb⁡A+(−1)logb⁡C =logbA−logbC=logb⁡A−logb⁡C

Expand the following: logb6xy=logb(6x)−logbylogb⁡6xy=logb⁡6x−logb⁡y

=logb6+logbx−logbylogb⁡6+logb⁡x−logb⁡y

Martha deposited $22,275.00 in account at 4.75% interest that in compound continuously. What amount does Mike have after 3.9 years?

A=22275.00(e)0.0475(3.9)A=22275.00(e)0.0475(3.9) A=$26,808.39A=$26,808.39

Kale received an inheritance and deposited into a money market account in the amount of $8,456.23, at a rate of 3.75% for 5.2 years compounded semi-annually how much money would Kale have?

A=8,456.63(1+0.03752)(2)(0.0375)A=8,456.63(1+0.03752)(2)(0.0375) A=$10,258.41A=$10,258.41

Evaluate the following: in(x) when x= 250 to the nearest hundredth.

In(250)=5.52

Rewrite the logarithmic function log3(81)=4log3⁡81=4 as an exponential function

base=3 exponent=4 argumentanswer=81base=3 exponent=4 argumentanswer=81 34=8134=81

Condense the Logarithmic Expression, solve the expression (find the x value or values, and check your work for valid answers.) log(X)+log(x−3)=1log⁡X+log⁡x−3=1

log(X)(x−3)=1log⁡Xx−3=1 logx2−3x=1log⁡x2−3x=1 x2−3x=10x2−3x=10 x−5+x+12x−5+x+12 x=5x=5

Condense the following: log2(x2)+12log2(x−1)−3log2((x+3)2)log2⁡(x2)+12log2⁡(x−1)−3log2⁡((x+3)2)

log2(x2)+12log2(x−1)−3log2((x+3)2)= log2x2+log2(x−1−−−−−√)−log2((x+3)6)log2⁡(x2)+12log2⁡(x−1)−3log2⁡((x+3)2)= log2⁡x2+log2⁡x−1−log2⁡((x+3)6) log2(x2)+log2(x−1−−−−−√)−log2((x+3)6)=log2(x2x−1−−−−−√)−log2((x+3)6) log2⁡(x2)+log2⁡x−1−log2⁡((x+3)6)=log2⁡x2x−1−log2⁡((x+3)6) log2(x−1−−−−−√)−log2((x+3)6)=log2x2x−1−−−−−√(x+3)6log2⁡x−1−log2⁡((x+3)6)=log2⁡x2x−1(x+3)6

Condense the Following: log3(5)+log3(8)−log3(2)log3⁡5+log3⁡(8)−log3⁡(2)

log3(5)+log3(8)=log3(5∗8)=log3(40)log3⁡5+log3⁡(8)=log3⁡5∗8=log3⁡(40) log3(40)−log32log3⁡(40)−log3⁡2 log3(40)−log32=log3(402)=log3(20)log3⁡(40)−log3⁡2=log3(⁡402)=log3⁡(20)

Evaluate f(x)=log(x)fx=log⁡x at the given value of x. Round your answer to three decimal places

x=1600=−2.778x=1600=−2.778