SOLUTION: Determine the positive root of the following equation: log3(c - 4) + log3(c + 6) = 4. (Please round your answer to one decimal place.) Answer

Question 453069: Determine the positive root of the following equation:
log3(c - 4) + log3(c + 6) = 4.

(Please round your answer to one decimal place.)

Answer

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
log3(c - 4) + log3(c + 6) = 4
log3(c - 4)(c + 6) = 4
(c - 4)(c + 6) = 3^4
c^2 + 6c - 4c -24 = 81
c^2 + 2c -105 = 0
apply the quadratic formula to find the roots:
c = {9.3, -11.3}
throw out the negative root leaving:
c = 9.3
.
details of quadratic to follow:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=424 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9.295630140987, -11.295630140987. Here's your graph:

RELATED QUESTIONS
Determine the positive solution to the following equation: log5(c - 2) + log5(c + 4) = 5. (answered by ewatrrr)

Solve the equation. Round answer to four decimal places.... (answered by nerdybill)

Solve the logarithmic equation for x. log3 4 + log3 x = log3 6 + log3(x −... (answered by stanbon,nakaguma)

Solve the following equation for x. Log3 (5x + 4 ) = 6 (answered by josgarithmetic)

Given the parent functions f(x) = log3 (5x − 5) and g(x) = log3 (x − 1), what (answered by ewatrrr)

solve the following logarithmic equation. Exact answers only. log3(x+4)=2+log3(x-20) (answered by Alan3354)

Please help with this: Found the x values if log3 3x - log3 (x-4) = 2 A)6 B)9 C)64 (answered by tommyt3rd)

Determine the larger root of the following equation: log(z) + log(z + 19) = 2 log(z +... (answered by ankor@dixie-net.com)

solve the following equation log3 (x+4)+log3... (answered by rothauserc)