What is the expression for f(x) when we rewrite 36^(x)*6^(x-2) as 6^(f(x)) ? f(x)=

Recognizing the power of 6: We need to express 36^(x)*6^(x-2) in the form of 6^(f(x)). First, we recognize that 36 is a power of 6, specifically 36 = 6^2.Rewriting 36^(x): Rewrite 36^(x) as (6^2)^(x) which simplifies to 6^(2x) by using the power of a power rule (a^(m))^n = a^(mn).Combining terms with the same base: Now we have 6^(2x) * 6^(x-2). We can combine these terms because they have the same base by adding the exponents, according to the rule a^m * a^n = a^(m+n).Adding the exponents: Add the exponents 2x and (x-2) to get a single exponent: 2x + (x - 2) = 2x + x - 2 = 3x - 2.Final expression and conclusion: Now we have 6^(3x - 2). This is the expression we were looking for, so we can say that f(x) = 3x - 2.

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What is the expression for
f(x) when we rewrite
36^(x)*6^(x-2) as
6^(f(x)) ?

f(x)=

What is the expression for $f(x)$ when we rewrite $36^{x} \cdot 6^{x-2}$ as $6^{f(x)}$ ? $\newline$ $f(x)=$

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Algebra 1

Compare linear and exponential growth

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Q. What is the expression for

f(x)

when we rewrite

36^{x} \cdot 6^{x-2}

6^{f(x)}

\newline

f(x)=

Recognizing the power of $6$ : We need to express $36^{x}\cdot6^{x-2}$ in the form of $6^{f(x)}$ . First, we recognize that $36$ is a power of $6$ , specifically $36 = 6^2$ .
Rewriting $36^{x}$ : Rewrite $36^{x}$ as $(6^2)^{x}$ which simplifies to $6^{2x}$ by using the power of a power rule $(a^{m})^{n} = a^{mn}$ .
Combining terms with the same base: Now we have $6^{2x} \times 6^{x-2}$ . We can combine these terms because they have the same base by adding the exponents, according to the rule $a^m \times a^n = a^{m+n}$ .
Adding the exponents: Add the exponents $2x$ and $(x-2)$ to get a single exponent: $2x + (x - 2) = 2x + x - 2 = 3x - 2$ .
Final expression and conclusion: Now we have $6^{(3x - 2)}$ . This is the expression we were looking for, so we can say that $f(x) = 3x - 2$ .