SOLUTION: log4 (x^2 + 6) = log4 5x how do i solve this???

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log4 (x^2 + 6) = log4 5x how do i solve this???      Log On


   

Question 211315: log4 (x^2 + 6) = log4 5x
how do i solve this???
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C%28x%5E2+%2B+6%29%29=log%284%2C%285x%29%29 Start with the given equation.


x%5E2%2B6=5x Equate the arguments.


Note: Remember that if log%28b%2C%28x%29%29=log%28b%2C%28y%29%29, then x=y


x%5E2%2B6-5x=0 Subtract 5x from both sides.


x%5E2-5x%2B6=0 Rearrange the terms.


Notice that the quadratic x%5E2-5x%2B6 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-5, and C=6


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%286%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-5, and C=6


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%286%29+%29%29%2F%282%281%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%281%29%286%29+%29%29%2F%282%281%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25-24+%29%29%2F%282%281%29%29 Multiply 4%281%29%286%29 to get 24


x+=+%285+%2B-+sqrt%28+1+%29%29%2F%282%281%29%29 Subtract 24 from 25 to get 1


x+=+%285+%2B-+sqrt%28+1+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%285+%2B-+1%29%2F%282%29 Take the square root of 1 to get 1.


x+=+%285+%2B+1%29%2F%282%29 or x+=+%285+-+1%29%2F%282%29 Break up the expression.


x+=+%286%29%2F%282%29 or x+=++%284%29%2F%282%29 Combine like terms.


x+=+3 or x+=+2 Simplify.


So the solutions are x+=+3 or x+=+2