What is the simplified base for the function f(x) = 2(3√27(2x)?
2
3
9
18
Answer:
option C is correct i.e. 9
Step-by-step explanation:
We have given that : \(f(x)=2 \sqrt[3]{27^{2x}}\)
To find : The simplified base of the function f(x)
Solution:
Now, we solve the equation
\(f(x)=2 \sqrt[3]{27^{2x}}\)
\(f(x)=2(27^x)^{\frac{2}{3}}\)
\(f(x)=2(3^{2x})\)
\(f(x)=2((3^2)^{x})\)
\(f(x)=2(9^{x})\)
Therefore, the simplified base of the function f(x) is 9
Answer:
Option C is correct
9 the simplified base for the given function f(x)
Step-by-step explanation:
Using exponent rules:
\((x^m)^n = x^{mn}\)
\(\sqrt[n]{x^b} = x^{\frac{b}{n}}\)
Given the function:
\(f(x) = 2\sqrt[3]{27^{2x}}\)
We can write 27 as:
\(27 = 3 \cdot 3 \cdot 3 = 3^3\)
then;
\(f(x) = 2\sqrt[3]{(3^3)^{2x}}\)
Apply the exponent rules:
\(f(x) = 2\sqrt[3]{3^{6x}}\)
Apply the exponent rules:
\(f(x) =2 \cdot (3^{6x})^{\frac{1}{3}} = 2 \cdot 3^{2x}\)
⇒\(f(x) = 2 \cdot (3^2)^x = 2 \cdot 9^x\)
⇒\(f(x) =2 \cdot 9^x\)
On comparing with exponential function \(f(x) = ab^x\) where, b is base of the exponent function, then
b = 9
Therefore, the simplified base for the given function is, 9