You can
put this solution on YOUR website!Applying "log rules":
log7 x + log7 (4x+21) = 3
log7 x(4x+21) = 3
x(4x+21) = 7^3
4x^2 + 84 = 343
4x^2 + 84 - 343 = 0
Solving using the quadratic equation yields:
x = {3.5, -24.5}
Throw out the negative solution leaving:
x = 3.5
.
Details of quadratic follows:
| 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=12544 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 3.5, -24.5.
Here's your graph:
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