The expression log 10^(x+2)- log 10^x is equivalent to???

recall that log x^y = y log x

rewriting...
(x+2)(log 10) - (x)(log 10)
=(2)(log 10)
IF the base is 10 then log 10 = 1.
In that case the above reduces to:
=2

67h

Oh, logarithms, my favorite! Strap in, it's about to get logarithmic!

First, let's break this expression down. We have log base 10 of 10 raised to the power of (x + 2), minus log base 10 of 10 raised to the power of x. Now, let me introduce you to a little log rule called the "subtraction rule."

According to this rule, when you subtract two logs with the same base, it's the same as taking the log of the quotient of the two numbers inside the logs. So, our expression can be rewritten as log base 10 of (10^(x + 2) / 10^x).

Now, let me simplify this further for you. Remember that an exponent of x + 2 means that we are multiplying 10 by itself (x + 2) times, while an exponent of x means we are multiplying 10 by itself x times.

So, we can rewrite the expression as log base 10 of (10 * 10 * ... * 10 (x + 2 times) / 10 * 10 * ... * 10 (x times)).

And guess what? When we divide two equal numbers, we get 1! So, our expression can be further simplified to log base 10 of 1.

Now, log base 10 of 1? That's a fancy way of saying "0"! So, the equivalent of log 10^(x+2) - log 10^x is simply 0.

Voila! And that, my friend, is logarithmic hilarity at its finest.

To simplify the expression log 10^(x+2) - log 10^x, we can use the logarithmic rule known as the quotient rule. According to the quotient rule, log(b) - log(a) is equal to log(b/a).

Using this rule, we can rewrite the expression as follows:

log 10^(x+2) - log 10^x = log (10^(x+2) / 10^x)

Now, in the denominator, we have 10^x divided by 10^x, which is equal to 1. So, we can further simplify the expression as:

log (10^(x+2) / 10^x) = log (10^2) = log 100

The final simplified expression is log 100.

To simplify the expression log 10^(x+2) - log 10^x, we can use logarithmic properties.

First, let's recall the properties of logarithms:
1. log(a * b) = log(a) + log(b)
2. log(a / b) = log(a) - log(b)
3. log(a^b) = b * log(a)

Using these properties, we can simplify the expression step by step:

log 10^(x+2) - log 10^x
= (x + 2) * log 10 - x * log 10 (using property 3)
= (x + 2) - x (since log 10 = 1)
= x + 2 - x
= 2

Therefore, the equation log 10^(x+2) - log 10^x is equivalent to 2.