Question

Solve log 1/100 = log(10x + 2). A. x = –4 B. x = 4 C. x = 0 D. x = –2

Answer 1

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 2

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.