To solve the equation [tex]\(\log_{10} x = 0.5\)[/tex], we need to understand the relationship between logarithms and exponents.
The logarithmic equation [tex]\(\log_{10} x = 0.5\)[/tex] means that [tex]\(10\)[/tex] raised to what power equals [tex]\(x\)[/tex] yields [tex]\(0.5\)[/tex].
This can be rewritten as an exponential equation:
[tex]\[ x = 10^{0.5} \][/tex]
Now, we need to interpret what [tex]\(10^{0.5}\)[/tex] means. The exponent [tex]\(0.5\)[/tex] can be understood as the square root of [tex]\(10\)[/tex], because:
[tex]\[ 10^{0.5} = \sqrt{10} \][/tex]
Therefore, we evaluate the square root of 10. After performing the calculation, the result is approximately:
[tex]\[ \sqrt{10} \approx 3.1622776601683795 \][/tex]
Thus, the value of [tex]\(x\)[/tex] is:
[tex]\[ x \approx 3.1622776601683795 \][/tex]
