Problemas
Solve for all values ofx log_(8)(3x^2+9x-20)=2 Answer Attempt 2 out of 3 Additional Solution (C) Rerhove Solution x=square , x=square
Roztwór
Cristian
veterano · Tutor durante 11 años
4.7
(205 Votos)
Respuesta
The solutions to the equation are
and
.
Explicación
## Step 1The given equation is \(log_{8}(3x^{2}+9x-20)=2\). To solve this equation, we need to convert the logarithmic equation into an exponential equation.### **The formula for converting a logarithmic equation to an exponential equation is
**## Step 2Applying the formula, we get
.## Step 3Simplify the equation to get
.## Step 4Rearrange the equation to get
.## Step 5Factor the quadratic equation to get \((3x-7)(x+12) = 0\).## Step 6Setting each factor equal to zero gives the solutions
and
.