Question

5 raised to (1+x) + 5 raised to (1-x) = 26, what is x?

Answer 1

5^1 + x + 5^1 - x = 26

5^1 × 5^x + 5^1 × 5^-x = 26

5^1 ( 5^x + 5^ - x ) = 26

5^1 ( 5^x + 1/5^x ) = 26

5^x + 1/5^x = 26/5

5^2x + 1 / 5^x = 26 /5

so

5^2x + 1 = 26

5^x = 5

x = 1

Answer 2

Heya

5^(1+x) + 5^(1-x) = 26

By laws of exponents

a^m × a^n = a^(m+n)

a^m/a^n = a^(m-n)

x= 1 / -1