If x is equal to log 10 base 5 then X + 1 by X + 2 is equal to
(x+1)(x+2)
= x^2 + 3x + 2
but x = log 5 10
x+1 = log 5 10 + log 5 5
= log 5 50
x+2 = log 5 10 + 2log 5 5
= log 5 10 + log 5 25
= log 5 250
(x+1)(x+2) = (log 5 50)(log 5 250)
= appr 8.338865
To find the value of X + 1 / X + 2, we need to substitute the value of x, which is equal to log base 5 of 10. So,
X + 1 / X + 2 = (log base 5 of 10 + 1) / (log base 5 of 10 + 2)
Now, let's calculate the value.
To find the value of X + 1 by X + 2, we first need to simplify the expression.
Given that x = log5(10), we can rewrite this as 5^x = 10.
Now let's substitute this value into the expression X + 1 by X + 2:
(X + 1) / (X + 2)
Since we know x = log5(10), we can substitute it into the expression:
(log5(10) + 1) / (log5(10) + 2)
To evaluate this expression further, we can use the properties of logarithms.
Using the property that log(a) + log(b) = log(a * b), we can rewrite the numerator as a single logarithm:
log5(10) + log5(5)
Since log5(5) is equal to 1, the numerator simplifies to:
log5(10 * 5) = log5(50)
Following the same process, the denominator simplifies to:
log5(10 * 5 * 5) = log5(250)
Therefore, the expression X + 1 by X + 2 can be simplified to:
log5(50) / log5(250)