Question

what power of 10 would make the equation true 2.103 * 10^? = 210300000

Answer 1

To solve the equation \( 2.103 \times 10^x = 210300000 \), we need to isolate \( x \).

1. First, divide both sides of the equation by \( 2.103 \):

\[
10^x = \frac{210300000}{2.103}
\]

2. Calculate the right-hand side:

\[
\frac{210300000}{2.103} \approx 99999999.999047
\]

3. Now express \( 99999999.999047 \) in scientific notation. We know that \( 10^8 = 100000000 \), so:

\[
99999999.999047 \approx 10^8
\]

4. Therefore, the equation can be approximated as:

\[
10^x \approx 10^8
\]

5. This implies that:

\[
x \approx 8
\]

So, the power of 10 that makes the equation true is approximately \( 8 \). Therefore, the final answer is:

\[
\boxed{8}
\]