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Answer :
To solve the equation [tex]\(5^{3x} \times 5^1 = 625\)[/tex], we can follow these steps:
1. Combine the Exponents:
[tex]\[
5^{3x} \times 5^1 = 5^{3x+1}
\][/tex]
This is based on the property of exponents that states [tex]\(a^m \times a^n = a^{m+n}\)[/tex].
2. Rewrite 625 as a Power of 5:
Notice that [tex]\(625 = 5^4\)[/tex].
3. Set the Exponents Equal:
Since the bases are the same (both sides have base 5), we can set the exponents equal to each other:
[tex]\[
3x + 1 = 4
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Subtract 1 from both sides:
[tex]\[
3x = 3
\][/tex]
- Divide both sides by 3 to isolate [tex]\(x\)[/tex]:
[tex]\[
x = 1
\][/tex]
Therefore, the solution to the equation is [tex]\(x = 1\)[/tex].
1. Combine the Exponents:
[tex]\[
5^{3x} \times 5^1 = 5^{3x+1}
\][/tex]
This is based on the property of exponents that states [tex]\(a^m \times a^n = a^{m+n}\)[/tex].
2. Rewrite 625 as a Power of 5:
Notice that [tex]\(625 = 5^4\)[/tex].
3. Set the Exponents Equal:
Since the bases are the same (both sides have base 5), we can set the exponents equal to each other:
[tex]\[
3x + 1 = 4
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Subtract 1 from both sides:
[tex]\[
3x = 3
\][/tex]
- Divide both sides by 3 to isolate [tex]\(x\)[/tex]:
[tex]\[
x = 1
\][/tex]
Therefore, the solution to the equation is [tex]\(x = 1\)[/tex].
Thank you for reading the article Solve for the unknown tex 5 3x times 5 prime 625 tex. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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