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Write the log equation as an exponential equation. You do not need to solve for x. log(x^(2)+3x+14)=(1)/(4) Answer:

Write the log equation as an exponential equation. You do not need to solve for x \mathrm{x} .\newlinelog⁡(x2+3x+14)=14 \log \left(x^{2}+3 x+14\right)=\frac{1}{4} \newlineAnswer:

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Q. Write the log equation as an exponential equation. You do not need to solve for x \mathrm{x} .\newlinelog⁡(x2+3x+14)=14 \log \left(x^{2}+3 x+14\right)=\frac{1}{4} \newlineAnswer:
  1. Apply Logarithmic Definition: To convert a logarithmic equation to an exponential equation, we use the definition of a logarithm. The logarithmic equation log⁡b(a)=c\log_b(a) = c can be rewritten as bc=ab^c = a. Here, the base bb of the logarithm is not specified, which means it is the common logarithm with base 1010. So, we can rewrite the given equation as 101/4=x2+3x+1410^{1/4} = x^2 + 3x + 14.
  2. Rewrite as Exponential Equation: Now, we express 101410^{\frac{1}{4}} as an exponential equation. Since 101410^{\frac{1}{4}} means the fourth root of 1010, we can write the exponential equation as 1014=x2+3x+1410^{\frac{1}{4}} = x^2 + 3x + 14 without any further simplification, as we are not asked to solve for xx.

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