rhunt568
Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

List the potential solutions to [tex]$2 \log x - \log 3 = \log 3$[/tex] from least to greatest.

[tex]x = \square[/tex] or [tex]x = \square[/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\( 2 \log x - \log 3 = \log 3 \)[/tex], we proceed as follows:

1. Isolate the logarithmic term involving [tex]\( x \)[/tex]:
[tex]\[ 2 \log x - \log 3 = \log 3 \][/tex]

2. Solve for [tex]\( 2 \log x \)[/tex] by adding [tex]\( \log 3 \)[/tex] to both sides of the equation:
[tex]\[ 2 \log x = \log 3 + \log 3 \][/tex]

3. Combine the logarithms on the right-hand side using the property [tex]\(\log a + \log b = \log(a \cdot b)\)[/tex]:
[tex]\[ 2 \log x = \log(3 \cdot 3) \][/tex]
[tex]\[ 2 \log x = \log 9 \][/tex]

4. Divide both sides by 2 to solve for [tex]\( \log x \)[/tex]:
[tex]\[ \log x = \log 9 / 2 \][/tex]
[tex]\[ \log x = \log 9^{1/2} \][/tex]

5. Simplify the right-hand side to get [tex]\( x \)[/tex]:
[tex]\[ \log x = \log 3 \][/tex]

6. Since the logarithm is the same on both sides, we equate the arguments:
[tex]\[ x = 3 \][/tex]

So, the solution to the equation [tex]\( 2 \log x - \log 3 = \log 3 \)[/tex] is [tex]\( x = 3 \)[/tex].

Thus, listing the potential solutions from least to greatest:
[tex]\[ x = 3 \][/tex]

DONE
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.