Simplify. Enter the result as a single logarithm with a coefficient of 1 log_(5)(7x^3)+log_(5)(8x^4)=square

## Step 1<br />We are given two logarithms with the same base, which are \(log_{5}(7x^{3})\) and \(log_{5}(8x^{4})\). According to the properties of logarithms, we can combine these two logarithms into one by using the product rule of logarithms.<br />### **The product rule of logarithms: \(log_{b}(M) + log_{b}(N) = log_{b}(MN)\)**<br />## Step 2<br />Applying the product rule to our given problem, we get:<br />### **\(log_{5}(7x^{3}) + log_{5}(8x^{4}) = log_{5}(7x^{3} * 8x^{4})\)**<br />## Step 3<br />Next, we simplify the expression inside the logarithm by multiplying the coefficients and adding the exponents of the variables.<br />### **\(log_{5}(7x^{3} * 8x^{4}) = log_{5}(56x^{7})\)**<br />## Step 4<br />Finally, we simplify the expression inside the logarithm by multiplying the coefficients and adding the exponents of the variables.<br />### **\(log_{5}(56x^{7}) = log_{5}(56x^{7})\)**