solve and round to the nearest thousandths

Question

solve and round to the nearest thousandths

a. 16-4ln(3x)=4

b. log(base 7)(x+1) + log(base 7)(x-1)= log (base 7)*3

Answer 1

a.  16-4ln(3x)=4

     4ln(3x) = 12

     ln(3x) = 3

     e³ = 3x

     x = e³/3

     x = 6.695

 

b.  log₇(x+1) + log₇(x-1) = log₇3

    log₇[(x+1)(x-1)] = log₇3

    log₇(x²-1) = log₇3

    x²-1 = 3

    x² = 4

    x=2

Answer 2

 

Hi Trevan,

 

a. 16 - 4ln(3x) = 4

 

    4 - ln(3x) = 1              (divide both sides by 4)

 

    ln(3x) = 3

 

    3x = e³

 

    x = e³/3

 

       = 6.695

 

b. log₇(x + 1) + log₇(x - 1) = log₇3

 

    log₇((x + 1)(x - 1)) = log₇3

 

    log₇(x² - 1) = log₇3

 

    x² - 1 = 3

 

    x² - 4 = 0

 

    (x + 2)(x - 2) = 0

 

    x = 2 or -2

 

    But, an argument of the logarithm needs to be positive

    only x = 2 can be the answer.