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 [tex]\log(\frac{1}{100})=\log(10^{x+2})[/tex]
To find : Solve the expression?
Solution :
Step 1 - Write the expression
[tex]\log(\frac{1}{100})=\log(10^{x+2})[/tex]
Step 2 - Using law of logarithms,
[tex]\log x=\log y\Rightarrow x=y[/tex]
Applying in the expression,
[tex]\frac{1}{100}=10^{x+2}[/tex]
Step 3 - Solve the equation,
[tex]10^{-2}=10^{x+2}[/tex]
Step 4 - The bases are equal, equate the exponents
[tex]-2=x+2[/tex]
[tex]x=-4[/tex]
Therefore, The solution of the expression is [tex]x=-4[/tex]
So, Option A is correct.
