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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) f(x) when we rewrite (149)x⋅(17)6x+11 \left(\frac{1}{49}\right)^{x} \cdot\left(\frac{1}{7}\right)^{6 x+11} as (17)f(x) \left(\frac{1}{7}\right)^{f(x)} ?\newlinef(x)= f(x)=

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Q. What is the expression for f(x) f(x) when we rewrite (149)x⋅(17)6x+11 \left(\frac{1}{49}\right)^{x} \cdot\left(\frac{1}{7}\right)^{6 x+11} as (17)f(x) \left(\frac{1}{7}\right)^{f(x)} ?\newlinef(x)= f(x)=
  1. Rewriting base 4949: We need to express the given function in terms of a single base to match the form (17)f(x)\left(\frac{1}{7}\right)^{f(x)}. Let's start by rewriting the base 4949 in terms of 77, since 4949 is 77 squared.
  2. Simplifying base 4949: The base 4949 can be written as 727^2. Therefore, (149)x\left(\frac{1}{49}\right)^x can be rewritten as (172)x\left(\frac{1}{7^2}\right)^x. This simplifies to (17)2x\left(\frac{1}{7}\right)^{2x} because when you raise a power to a power, you multiply the exponents.
  3. Combining the bases: Now we have (17)2x⋅(17)6x+11\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.
  4. Simplifying the exponents: Adding the exponents, we get (17)2x+6x+11\left(\frac{1}{7}\right)^{2x + 6x + 11}. Simplifying the exponents, we have (17)8x+11\left(\frac{1}{7}\right)^{8x + 11}.
  5. Determining f(x)f(x): Now that we have the expression in the form (17)something\left(\frac{1}{7}\right)^{\text{something}}, we can see that ＂something＂ is our f(x)f(x). Therefore, f(x)=8x+11f(x) = 8x + 11.

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