solve the following with steps please

Question

4^x= 3+18(4^-x)

Answer 1

4^x = 3 + 18 (4^-x)

(4^x) 4^x = 3 (4^x) + 18 (4^-x) (4^x)

(4^x)² = 3 (4^x) + 18

(4^x)² - 3 (4^x) - 18 = 0

(4^x + 3) (4^x - 6) = 0

4^x + 3 = 0 or 4^x - 6 = 0

4^x = -3 or 4^x = 6

ln(4^x) = ln(-3) or ln(4^x) = ln(6)

x ln(4) = ln(-3) or x ln(4) = ln(6)

x = ln(-3) / ln(4) or x = ln(6) / ln(4)

x = no real solution or x = ln(6) / ln(4)

So x = ln(6) / ln(4) is the only real solution.