Question

An exponential function "f" is defined by f(x)=7(1.5)^x-6. if f(k)=91, then what is the value of k?

Answer 1

you are solving

7(1.5)^(k-6) = 91
1.5^(k-6) = 13

take log of both sides
log [1.5^(k-6)] = log 13
(k-6)[log 1.5] = log 13
k-6 = log13/log1.5 = 6.3259
k = 12.3259

check
7(1.5^6.3259)
= 7(12.99977) = 90.9984 (not bad)

Answer 2

log1/7(x^2=x)-log1/7(x^2-x)=-1