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Find the value of x to make this exponential equation true…

5^x ÷ 5^5 = 5^12

3 answers

To solve the equation \( \frac{5^x}{5^5} = 5^{12} \), we can use properties of exponents.

Recall the property of exponents that states:

\[ \frac{a^m}{a^n} = a^{m-n} \]

This allows us to simplify the left side of the equation:

\[ \frac{5^x}{5^5} = 5^{x-5} \]

Now, we can rewrite the equation as:

\[ 5^{x-5} = 5^{12} \]

Since the bases are the same, we can set the exponents equal to each other:

\[ x - 5 = 12 \]

To find \( x \), we can solve for it:

\[ x = 12 + 5 \] \[ x = 17 \]

Thus, the value of \( x \) that makes the equation true is

\[ \boxed{17} \]

Can you do it like an 8th grader

Sure! Let’s break it down step by step in a simpler way.

We have the equation:

\[ \frac{5^x}{5^5} = 5^{12} \]

  1. Understanding the left side: When you divide powers of the same base (here, the base is 5), you can subtract the exponents. So, we can rewrite the left side:

    \[ \frac{5^x}{5^5} = 5^{x - 5} \]

  2. Now the equation looks like this:

    \[ 5^{x - 5} = 5^{12} \]

  3. Since both sides have the same base (5), we can set the exponents equal to each other:

    \[ x - 5 = 12 \]

  4. Now, we just need to solve for \( x \). To do that, we add 5 to both sides of the equation:

    \[ x - 5 + 5 = 12 + 5 \] \[ x = 17 \]

So, the value of \( x \) that makes the equation true is

\[ \boxed{17} \]