Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To solve the equation [tex]\(\log _{\sqrt{5}}(x) = 2\)[/tex], we will perform the following steps:
1. Understand the meaning of the logarithmic equation:
The equation [tex]\(\log _{\sqrt{5}}(x) = 2\)[/tex] means that [tex]\(\sqrt{5}\)[/tex] raised to the power of [tex]\(2\)[/tex] results in [tex]\(x\)[/tex].
In general, if [tex]\( \log_b(a)=c \)[/tex], it means [tex]\( b^c = a \)[/tex].
2. Convert the logarithmic equation to an exponential form:
Given [tex]\(\log _{\sqrt{5}}(x) = 2\)[/tex], we can rewrite it as:
[tex]\[ (\sqrt{5})^2 = x \][/tex]
3. Simplify the right-hand side:
We need to calculate [tex]\((\sqrt{5})^2\)[/tex]. By the properties of exponents, we know:
[tex]\[ (\sqrt{5})^2 = 5 \][/tex]
4. Write the final solution:
Hence, we have:
[tex]\[ x = 5 \][/tex]
Therefore, the solution to the equation [tex]\(\log _{\sqrt{5}}(x) = 2\)[/tex] is [tex]\(x = 5\)[/tex].
1. Understand the meaning of the logarithmic equation:
The equation [tex]\(\log _{\sqrt{5}}(x) = 2\)[/tex] means that [tex]\(\sqrt{5}\)[/tex] raised to the power of [tex]\(2\)[/tex] results in [tex]\(x\)[/tex].
In general, if [tex]\( \log_b(a)=c \)[/tex], it means [tex]\( b^c = a \)[/tex].
2. Convert the logarithmic equation to an exponential form:
Given [tex]\(\log _{\sqrt{5}}(x) = 2\)[/tex], we can rewrite it as:
[tex]\[ (\sqrt{5})^2 = x \][/tex]
3. Simplify the right-hand side:
We need to calculate [tex]\((\sqrt{5})^2\)[/tex]. By the properties of exponents, we know:
[tex]\[ (\sqrt{5})^2 = 5 \][/tex]
4. Write the final solution:
Hence, we have:
[tex]\[ x = 5 \][/tex]
Therefore, the solution to the equation [tex]\(\log _{\sqrt{5}}(x) = 2\)[/tex] is [tex]\(x = 5\)[/tex].
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.