Verified Answer :

supercait12

Your answer would be Dx=-4. 

Here is why: log implies that the base is 10log10n=nlog10=n

Using the above two facts, you will be able to get:
1100=10−2, so log(1100)=−2
log10x+2=x+2

x+2=−2, so x=−4

Answer:

Option A - x=-4

Step-by-step explanation:

Given : Expression \(\log(\frac{1}{100})=\log(10^{x+2})\)

To find : Solve the expression?

Solution :

Step 1 - Write the expression

\(\log(\frac{1}{100})=\log(10^{x+2})\)

Step 2 - Using law of logarithms,

\(\log x=\log y\Rightarrow x=y\)

Applying in the expression,

\(\frac{1}{100}=10^{x+2}\)

Step 3 - Solve the equation,

\(10^{-2}=10^{x+2}\)

Step 4 - The bases are equal, equate the exponents

\(-2=x+2\)

\(x=-4\)

Therefore, The solution of the expression is \(x=-4\)

So, Option A is correct.

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