What is the expression for f(x) when we rewrite ((1)/(49))^(x)*((1)/(7))^(6x+11) as ((1)/(7))^(f(x)) ? f(x)=

Rewriting base 49: We need to express the given function in terms of a single base to match the form ((1)/(7))^(f(x)). Let's start by rewriting the base 49 in terms of 7, since 49 is 7 squared.Simplifying base 49: The base 49 can be written as 7^2. Therefore, ((1)/(49))^x can be rewritten as ((1)/(7^2))^x. This simplifies to ((1)/(7))^(2x) because when you raise a power to a power, you multiply the exponents.Combining the bases: Now we have ((1)/(7))^(2x) * ((1)/(7))^(6x+11). Since the bases are the same, we can add the exponents to combine them into a single expression.Simplifying the exponents: Adding the exponents, we get ((1)/(7))^(2x + 6x + 11). Simplifying the exponents, we have ((1)/(7))^(8x + 11).Determining f(x): Now that we have the expression in the form ((1)/(7))^(something), we can see that ＂something＂ is our f(x). Therefore, f(x) = 8x + 11.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the expression for
f(x) when we rewrite
((1)/(49))^(x)*((1)/(7))^(6x+11) as
((1)/(7))^(f(x)) ?

f(x)=

What is the expression for $f(x)$ when we rewrite $\left(\frac{1}{49}\right)^{x} \cdot\left(\frac{1}{7}\right)^{6 x+11}$ as $\left(\frac{1}{7}\right)^{f(x)}$ ? $\newline$ $f(x)=$

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. What is the expression for

f(x)

when we rewrite

\left(\frac{1}{49}\right)^{x} \cdot\left(\frac{1}{7}\right)^{6 x+11}

\left(\frac{1}{7}\right)^{f(x)}

\newline

f(x)=

Rewriting base $49$ : We need to express the given function in terms of a single base to match the form $\left(\frac{1}{7}\right)^{f(x)}$ . Let's start by rewriting the base $49$ in terms of $7$ , since $49$ is $7$ squared.
Simplifying base $49$ : The base $49$ can be written as $7^2$ . Therefore, $\left(\frac{1}{49}\right)^x$ can be rewritten as $\left(\frac{1}{7^2}\right)^x$ . This simplifies to $\left(\frac{1}{7}\right)^{2x}$ because when you raise a power to a power, you multiply the exponents.
Combining the bases: Now we have $\left(\frac{1}{7}\right)^{2x} \cdot \left(\frac{1}{7}\right)^{6x+11}$ . Since the bases are the same, we can add the exponents to combine them into a single expression.
Simplifying the exponents: Adding the exponents, we get $\left(\frac{1}{7}\right)^{2x + 6x + 11}$ . Simplifying the exponents, we have $\left(\frac{1}{7}\right)^{8x + 11}$ .
Determining $f(x)$ : Now that we have the expression in the form $\left(\frac{1}{7}\right)^{\text{something}}$ , we can see that ＂something＂ is our $f(x)$ . Therefore, $f(x) = 8x + 11$ .