how can you simplify this??
log10(10^.5)
log10 as in log base 10
By definition:
Log_10[10^(x)] = x
ok, but it is 10 to the 1/2 power, not x
how would you simplify it then?
That's then the special case of x = 1/2:
If for all x:
Log_10[10^x] = x,
then for x = 1/2 this implies:
Log_10[10^(1/2)] = 1/2
To simplify the expression log10(10^.5), you can use the fact that log10(10^x) = x. In this case, since 10^.5 equals the square root of 10, you can rewrite the expression as log10(sqrt(10)).
Since log10(10^x) = x, we can say that log10(sqrt(10)) = x. Now, we want to find the value of x that satisfies this equation.
To do that, we can recall that log10(sqrt(10)) can be rewritten as the exponent form 10^x = sqrt(10).
Now, we can solve for x by raising both sides of the equation to the power of 2 (so we can eliminate the square root):
(10^x)^2 = (sqrt(10))^2
10^(2x) = 10
Now, we can equate the exponents:
2x = 1
Divide both sides by 2:
x = 1/2
So, the simplified version of log10(10^.5) is 1/2.