Find the exact solution to the equation below Do not give a

Find the exact solution to the equation below. (Do not give a decimal approximation.)

Find the exact solution to the equation below. (Do not give a decimal approximation.)

Using laws of logarithms, write the expression below as a single logarithm.

Using laws of logarithms, write the expression below using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers.

Using laws of logarithms, write the expression below using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers.

ln(A-B)=

Solution

1) log(2x -1) - log( x-1) = 1

Using the Log Property : logA + logB -logC = log(A*B/C)

log( 2x -1)/(x-1) =1

(2x-1)(x-1) = 10

2x^2 -3x +1 =10

2x^2 -3x -9 =0

2x^2 -6x +3x -9 =0

2x( x-3) + 3(x-3) =0

(2x +3) =0 and x=3

x= -3/2 and x=3

2) 340 = 58 (2)^t/11

taking natural log of both sides:

ln(340 = ln{ 58 (2)^t/11}

ln(340) = ln58 + ln(2^t/11)

= ln58 + (t/11)ln2

t/11 = { ln340 - ln58 }/ln2

t = 11 { ln340 - ln58 }/ln2 = 28.06

3. 2ln( 5x +8) = 30

ln(5x +8) = 15

(5x +8) = e^15

5x = e^15 -8

x = ( e^15 -8)/5

4. 1/3log8 -1/2 log36

Using the Log Property : logA + logB -logC = log(A*B/C)

log8^1/3 - log36^1/2

log{ 8^1/3/36^1/2}

= log2^3*1/3 / 6^2*1/2 }

= log2 /6

=log(1/3)

= -log3