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Answer:
t = 7
Step-by-step explanation:
You can use your knowledge of powers of 2, or you can use logarithms to find the value of t.
2^1 = 2
2^2 = 4
2^4 = 16
128 = 16×4×2 = (2^4)(2^2)(2^1) = 2^(4+2+1) = 2^7
Now, the equation is ...
f(t) = 2^t = 2^7
Equating exponents, we have ...
t = 7
Taking the log of both sides of the equation ...
2^t = 128
we have ...
t×log(2) = log(128)
t = log(128)/log(2) = 7 . . . . . divide by the coefficient of t
The value of t is 7.
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Additional comment
The relevant rule of exponents is ...
(a^b)(a^c) = a^(b+c)
The relevant rule of logarithms is ...
log(a^b) = b×log(a)