SOLUTION: Solve the logarithmic equation algebraically. Round to three decimal places.
log base(4)5x- log(4)(6+sq root of x)=2
Algebra.Com
Question 369496: Solve the logarithmic equation algebraically. Round to three decimal places.
log base(4)5x- log(4)(6+sq root of x)=2
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
Solve the logarithmic equation algebraically. Round to three decimal places.
log base(4)5x- log(4)(6+sq root of x)=2
log4 (5x) - log4 (6 + sqrt(x)) = 2
logarithmic rule: logb (m/n) = logb (m) - logb (n)
log4 (5x/(6 + sqrt(x))) = 2
logarithmic rule: logb (m) = logk (m)/ logk b, where k is your new base
log4 (5x/(6 + sqrt(x))) = [log10 (5x/(6 + sqrt(x)))] / log10 (4) = 2
log10 (5x/(6 + sqrt(x))) = 2log10 (4)
logarithmic rule: nlogb (m) = logb (m^n)
4^2 = 16
log10 (5x/(6 + sqrt(x))) = log10 (16)
5x/(6 + sqrt(x)) = 16
5x = 16(6 + sqrt(x))
5x = 96 + 16sqrt(x)
5x - 96 = 16sqrt(x)
(5x - 96)^2 = (16sqrt(x))^2 (square both sides)
25x^2 - 960x + 9216 = 256x
25x^2 - 1216x + 9216 = 0, solve this and determine which root works
use quadratic formula, a = 25, b = -1216, c = 9216
557056 = 128 * 128 * 34
x1 = 608/25 + (64/25)sqrt(34)
x1 = 24.32 + 2.56sqrt(34)
x1 = 39.247237 to 6 places = 39.247 to 3 places
x2 = 24.32 - 2.56sqrt(34)
x2 = 9.392763 to 6 places = 9.392 to 3 places
check log10 (5x/(6 + sqrt(x))) = log10 (16)
log10 (16) = 1.204120 to 6 places
x1 gives log10 (16) = log10 (16), x1 works
x2 gives log10 (5.180921) which does not equal log10 (16), x2 does not work
answer for x is 39.247 to 3 places
RELATED QUESTIONS
Solve the logarithmic equation algebraically. Approximate the result to three decimal... (answered by LinnW)
Please help me solve this question: Solve the logarithmic equation algebraically.... (answered by Alan3354)
Solve the logarithmic equation algebraically.Approximate the result to three decimal... (answered by lwsshak3)
Solve the logarithmic equation.
Express irriational solutions in exact form and as a... (answered by stanbon)
Please help me solve this equation: Solve the logarithmic equation algebraically.... (answered by robertb)
Solve the logarithmic equation algebraically. Show steps
log x=-4
(answered by jsmallt9)
Solve the logarithmic equation:
Log
(base 2(x+3)+log(base... (answered by lwsshak3)
Solve the exponential equation. Round the result to 3 decimal places.
1.... (answered by stanbon)
ln(x) + ln(x – 5) = 4
Solve the logarithmic equation algebraically
Approximate the... (answered by jsmallt9)