Answer :

To solve the equation [tex]\(5^{3x} \times 5^1 = 625\)[/tex], follow these steps:

1. Combine Exponents for the Same Base:

The equation [tex]\(5^{3x} \times 5^1 = 625\)[/tex] can be simplified using the property of exponents that states:

[tex]\[a^m \times a^n = a^{m+n}\][/tex]

Apply this to the equation:

[tex]\[5^{3x+1} = 625\][/tex]

2. Express 625 as a Power of 5:

Next, recognize that 625 is a power of 5. To find what power, note that:

[tex]\[5 \times 5 = 25\][/tex]
[tex]\[25 \times 5 = 125\][/tex]
[tex]\[125 \times 5 = 625\][/tex]

Therefore, [tex]\(625 = 5^4\)[/tex].

3. Set the Exponents Equal:

Now that we have [tex]\(5^{3x+1} = 5^4\)[/tex], and since the bases are the same, we can set the exponents equal to each other:

[tex]\[3x + 1 = 4\][/tex]

4. Solve for [tex]\(x\)[/tex]:

Solve the equation for [tex]\(x\)[/tex]:

[tex]\[
3x + 1 = 4
\][/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 tex x tex in the equation tex 5 3x times 5 1 625 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!

Rewritten by : Jeany

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