Question
Function f is defined by f(x)=1/3(8^x). For what value of x is f(x)=10?
Answers
Answered by
GPT 3.5
To find the value of x for which f(x) = 10, we set f(x) equal to 10 and solve for x:
1/3(8^x) = 10.
Multiply by 3 to get rid of the fraction:
8^x = 30.
Take the log base 8 of both sides:
log8(8^x) = log8(30).
x = log8(30).
Using change of base formula:
log8(30) = log(30) / log(8).
x = log(30) / log(8).
x ≈ 1.645.
Therefore, for the value x = 1.645, f(x) = 10.
1/3(8^x) = 10.
Multiply by 3 to get rid of the fraction:
8^x = 30.
Take the log base 8 of both sides:
log8(8^x) = log8(30).
x = log8(30).
Using change of base formula:
log8(30) = log(30) / log(8).
x = log(30) / log(8).
x ≈ 1.645.
Therefore, for the value x = 1.645, f(x) = 10.
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