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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) f(x) when we rewrite 36x⋅6x−2 36^{x} \cdot 6^{x-2} as 6f(x) 6^{f(x)} ?\newlinef(x)= f(x)=

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Q. What is the expression for f(x) f(x) when we rewrite 36x⋅6x−2 36^{x} \cdot 6^{x-2} as 6f(x) 6^{f(x)} ?\newlinef(x)= f(x)=
  1. Recognizing the power of 66: We need to express 36x⋅6x−236^{x}\cdot6^{x-2} in the form of 6f(x)6^{f(x)}. First, we recognize that 3636 is a power of 66, specifically 36=6236 = 6^2.
  2. Rewriting 36x36^{x}: Rewrite 36x36^{x} as (62)x(6^2)^{x} which simplifies to 62x6^{2x} by using the power of a power rule (am)n=amn(a^{m})^{n} = a^{mn}.
  3. Combining terms with the same base: Now we have 62x×6x−26^{2x} \times 6^{x-2}. We can combine these terms because they have the same base by adding the exponents, according to the rule am×an=am+na^m \times a^n = a^{m+n}.
  4. Adding the exponents: Add the exponents 2x2x and (x−2)(x-2) to get a single exponent: 2x+(x−2)=2x+x−2=3x−22x + (x - 2) = 2x + x - 2 = 3x - 2.
  5. Final expression and conclusion: Now we have 6(3x−2)6^{(3x - 2)}. This is the expression we were looking for, so we can say that f(x)=3x−2f(x) = 3x - 2.

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