Find the exact solution to the equation below. (Do not give a decimal approximat
ID: 3423811 • Letter: F
Question
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)=
Explanation / Answer
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
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