-(-sqrt-10%5E-2-frac-1-2-log-(16)-%3D-).jpeg "(iii) ( Sqrt 10^ 2 Frac 1 2 Log (16) = )")
Simplifying the Expression: $(\sqrt{10^2}) \frac{1}{2} \log (16)$
In this article, we will simplify the given expression: $(\sqrt{10^2}) \frac{1}{2} \log (16)$. Let's break it down step by step.
Step 1: Simplify the Square Root The first part of the expression is $(\sqrt{10^2})$. To simplify this, we can use the property of exponents that states: $\sqrt{x^2} = x$. Therefore, we can simplify $(\sqrt{10^2})$ to:
$(\sqrt{10^2}) = 10$
Step 2: Evaluate the Logarithm The next part of the expression is $\log (16)$. To evaluate this, we need to find the power to which the base must be raised to equal 16. Since 16 is a power of 2 (i.e., $2^4 = 16$), we can write:
$\log (16) = \log (2^4) = 4 \log (2)$
Step 3: Simplify the Fraction Now, we have the expression: $10 \cdot \frac{1}{2} \cdot 4 \log (2)$. To simplify this fraction, we can multiply the numerator by the denominator:
$10 \cdot \frac{1}{2} \cdot 4 \log (2) = 20 \log (2)$
Therefore, the simplified expression is:
$(\sqrt{10^2}) \frac{1}{2} \log (16) = 20 \log (2)$
