To solve the equation [tex]\(2 \log x = \log 36\)[/tex], follow these steps:
1. Understand the given equation:
- The equation provided is [tex]\(2 \log x = \log 36\)[/tex].
2. Use logarithm properties:
- One of the properties of logarithms states that [tex]\(a \log b = \log(b^a)\)[/tex].
- Apply this property to the left side of the equation: [tex]\(2 \log x = \log(x^2)\)[/tex].
3. Rewrite the equation:
- Using the property from step 2, the equation becomes [tex]\(\log(x^2) = \log 36\)[/tex].
4. Set the arguments of the logarithms equal:
- If [tex]\(\log a = \log b\)[/tex], then [tex]\(a\)[/tex] must equal [tex]\(b\)[/tex].
- Thus, [tex]\(x^2 = 36\)[/tex].
5. Solve for [tex]\(x\)[/tex]:
- To find [tex]\(x\)[/tex], take the square root of both sides: [tex]\(x = \sqrt{36}\)[/tex].
6. Evaluate the square root:
- The square root of 36 is 6: [tex]\(x = 6\)[/tex].
7. Check the multiple-choice answers:
- [tex]\(x = 1.6\)[/tex]
- [tex]\(x = 6\)[/tex]
- [tex]\(x = 18\)[/tex]
- [tex]\(x = 72\)[/tex]
From the provided answers, the correct solution is [tex]\(x = 6\)[/tex].
