Exercise
$\log\left(x^2+4x\right)=\log\left(21\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the logarithmic equation log(x^2+4*x)=log(21). For two logarithms of the same base to be equal, their arguments must be equal. In other words, if \log(a)=\log(b) then a must equal b. Move everything to the left hand side of the equation. Factor the trinomial x^2+4x-21 finding two numbers that multiply to form -21 and added form 4. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values.
Solve the logarithmic equation log(x^2+4*x)=log(21)
Final answer to the exercise
$x=3,\:x=-7$