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1. Solve for the unknown

a) $5^{3x} \times 5^1 = 625$

Answer :

To solve the equation $5^{3x} \times 5^1 = 625$, we can start by simplifying and analyzing the equation step by step.


  1. Simplify the expression on the left-hand side:

    Remember the rule of exponents: [tex]a^m \times a^n = a^{m+n}[/tex]. So, we can combine the exponents on the left side:

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

    Now the equation becomes:
    [tex]5^{3x+1} = 625[/tex]


  2. Express 625 as a power of 5:

    We know $625[tex]is a power of $5[/tex]. Let's express it as such:

    [tex]625 = 5^4[/tex]

    Now the equation is:
    [tex]5^{3x+1} = 5^4[/tex]


  3. Set the exponents equal to each other:

    Since the bases are the same, the exponents must be equal:

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


  4. Solve for [tex]x[/tex]:

    Subtract $1$ from both sides:

    [tex]3x = 3[/tex]

    Divide both sides by $3$:

    [tex]x = 1[/tex]



Therefore, the value of the unknown [tex]x[/tex] is 1.

This step-by-step explanation uses the rules of exponents and simple algebraic manipulation to find the solution. Understanding these principles is crucial for solving exponential equations effectively.

Thank you for reading the article 1 Solve for the unknowna 5 3x times 5 1 625. 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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