If x+ ₁₅ (1+3^x )=x ₁₅ 5+ ₁₅ 12 , where x is an integer, then what is x equal to?

Step-by-step solution

aligned & x+ ₁₅ (1+3^x )=x ₁₅ 5+ ₁₅ 12 & x ₁₅ 15+ ₁₅ (1+3^x )=x ₁₅ 5+ ₁₅ 12 & ( ₁₅ 15=1 ) & ₁₅ 15^x+ ₁₅ (1+3^x )= ₁₅ 5^x+ ₁₅ 12 & ₁₅ 15^x (1+3^x )= ₁₅ (5^x 12 ) & ( a+ b= a b) aligned aligned & 15^x (1+3^x )=5^x 12 & 3^x (1+3^x )=12 & 3^x+3^ 2 x =12 aligned x =1 satisfies the above equation.