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

## Step 1<br />The 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.<br /><br />### **The formula for converting a logarithmic equation to an exponential equation is \(log_{b}a = c \Rightarrow b^{c} = a\)**<br /><br />## Step 2<br />Applying the formula, we get \(8^{2} = 3x^{2}+9x-20\).<br /><br />## Step 3<br />Simplify the equation to get \(64 = 3x^{2}+9x-20\).<br /><br />## Step 4<br />Rearrange the equation to get \(3x^{2}+9x-84 = 0\).<br /><br />## Step 5<br />Factor the quadratic equation to get \((3x-7)(x+12) = 0\).<br /><br />## Step 6<br />Setting each factor equal to zero gives the solutions \(x = 7/3\) and \(x = -12\).