For which value of a will 8 x 10^3 be 10 times larger than 8 x 10^a?

3 answers

To determine the value of \( a \) for which \( 8 \times 10^3 \) is 10 times larger than \( 8 \times 10^a \), we can set up the equation:

\[ 8 \times 10^3 = 10 \times (8 \times 10^a) \]

First, we simplify the right-hand side:

\[ 8 \times 10^3 = 80 \times 10^a \]

Next, we divide both sides by 8:

\[ 10^3 = 10 \times 10^a \]

This simplifies to:

\[ 10^3 = 10^{a+1} \]

Now, we can equate the exponents (since the bases are the same):

\[ 3 = a + 1 \]

Solving for \( a \):

\[ a = 3 - 1 = 2 \]

Thus, the value of \( a \) is

\[ \boxed{2} \]

That's correct thank you!

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