Use the like bases property to solve the equation

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Ask by Lowe Schwartz. in the United States

Mar 13,2025

Question

Use the like bases property to solve the equation $$ 6(10)^{x}+21=60021 $$ $$ x=\square $$ Question Help: Video Submit Question

UpStudy AI · Accepted Answer

To solve the equation $$ 6(10)^{x} + 21 = 60021 $$, we will follow these steps:

1. **Isolate the term with the exponent**: Start by subtracting 21 from both sides of the equation.
   
   $$
   6(10)^{x} = 60021 - 21
   $$

2. **Calculate the right side**: Perform the subtraction.

$$
   60021 - 21 = 60000
   $$

So, the equation now is:

$$
   6(10)^{x} = 60000
   $$

3. **Divide both sides by 6**: This will isolate $$ (10)^{x} $$.

$$
   (10)^{x} = \frac{60000}{6}
   $$

4. **Calculate the division**:

$$
   \frac{60000}{6} = 10000
   $$

Now, we have:

$$
   (10)^{x} = 10000
   $$

5. **Express 10000 as a power of 10**: We know that $$ 10000 = 10^4 $$.

$$
   (10)^{x} = (10)^{4}
   $$

6. **Set the exponents equal to each other**: Since the bases are the same, we can equate the exponents.

$$
   x = 4
   $$

Thus, the solution to the equation is:

$$
x = 4
$$
$$ x = 4 $$

Use the like bases property to solve the equation

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