The given equation is
[tex]\log_{5}15=x+3\\\\ \frac{\log(5\times 3)}{\log5}=x+3 \\\\ \frac{\log5 + \log3}{\log5}= x +3\\\\ 1+\log_{5}3=x+3\\\\ x= -3 +1+\log_{5}3 \\\\ x= -2 +\log_{5}3[/tex] →→taking the constant 3 on another side of equation
x= -2 + [tex]\frac{0.4771}{0.6990}[/tex]
x = -2 + 0.6825 = -1.3175
x= -1.3175 (approx)
