If `log_(10)a=b`, then fnd the value of `10^(3b)` in terms of a.

Options

A. A)`a^(3)`
B. B)3a
C. C)`axx1000`
D. D)`axx100`

Answer

To solve the problem, we start with the given equation:

1. **Given:** \( \log_{10} a = b \)

This means that \( a \) can be expressed in terms of \( b \) using the definition of logarithms.

2. **Convert the logarithmic equation to exponential form:**
\[ a = 10^b \]

3. **Now, we need to find \( 10^{3b} \):**
\[ 10^{3b} = (10^b)^3 \]

Here, we are using the property of exponents that states \( (x^m)^n = x^{m \cdot n} \).

4. **Substituting \( 10^b \) with \( a \):**
\[ 10^{3b} = (10^b)^3 = a^3 \]

5. **Final result:**
\[ 10^{3b} = a^3 \]

Thus, the value of \( 10^{3b} \) in terms of \( a \) is \( a^3 \).