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