Let 2^a = 5 and 2^b = 10. Using exponent rules, solve the equation in terms of a and b.

Question

10^x =(1/64)

Answer 1

1/64 = 1/2^6
so
10^x = 2^-6

(2^b)^x = 2^-6
2^bx = 2^-6
so
b x = -6
but 2^b = 2*5 = 2*2^a = 2^(a+1)
so
b = a+1
(a+1)x = -6