Exponential and logarithmic functions help

Question

1.) Log7 x^8 - log7 x^5 =11
2.) Log 1/2(1/64)
3.) Ln (x+2) =3
4.) Which is the inverse of f(x)=6^x?
a. f^1(x)=6 log^6
b. f^1(x)= log 6x
c. f^1(x)=(log x)/6
d. f^1(x)= log x^6
5.) Log 3 32.3+log 3 7.5
Express the above expression as a simple logarithm.
A. log 6 39.9
B. log 9 243
C. log 3 39.9
D. log 3 243
E. log 3 4.32
Then simplify. Enter your numerical answer. Round your answer to the nearest tenth if necessary.
6.) 3^2x=30
a. log 3 60
b. 2 log 3 30
c. (log 3 30)/2
d. log 3 15
7.) log8 8
8.) Which is the logarithmic form of 2^10=1024?
a. log 10 2=1024
b. log 10 1024=2
c. log 2 10=1024
d. log 2 1024=10
9.) solve for x: 3log4 6 - log4 8 = log4 x
10.) solve for x: log2 (3x-4) + log2 (5x-2) =4
11.) write the inverse of the function: f(x)=-(1/5)x+3

Answer 1

 

1) log7(x^8)-log7(x^5)=11

    log7(x^8/x^5)=11

    log7(x^3)=11

     7^11=x^3

     7^(11/3)=x, or

     7^11=1,977,326,743

     x^3=1,977,326,743

         x=1255.14185854

 

2) log1/2(1/64)

    log1/2(1/64)=x

    (1/2)^x=1/64

     64=2^6

      x=6

 

3) ln(x+2)=3

    e^3=x+2

    e^3-2=x

    20.0855369232-2=x

    18.0855369232=x

 

5) log3(32.4)+log3(7.5)

    log3(32.4*7.5)=log3(243) which is D)

    log3(243)=x, 3^x=243

    243=3*81=3*9*9=3*3*3*3*3=3^5

    3^x=3^5, x=5

 

6) 3^2x=30

    take log3 on both sides

    log3(3^2x)=log3(30)

    2xlog3(3)=log3(30)

    2x=log3(30)

     x=log3(30)/2, which is C)

 

 7) log8(8)=x implies 8^x=8, x=1

 

 8) D)

 

 9) 3log4(6)-log4(8)=log4(x)

       log4(6^3)-log4(8)=log4(x)

       log4(6^3/8)=log4(x)

              6^3/8=x

              216/8=x

                   27=x

10) log2(3x-4)+log2(5x-2)=4

      log2[(3x-4)(5x-2)]=4

      2^4=(3x-4)(5x-2)

        16=15x^2-26x+8

         15x^2-26x-8=0

         (15x+4)(x-2)=0

          x-2=0

          x=2

 

11) f^(-1)=(y-3)/(-1/5)

      f^(-1)=-5(y-3)