Combine into one log:
log
√
x + 1
+ 9 log x
i.e. rewrite as an expression of the form log u, where u is a function of x.
did you mean:
log √(x+1) + 9logx ??
then
= log √(x+1) + log x^9
= log ( x^9 √(x+1) )
To combine the given logarithmic expressions into one log expression, we can use the properties of logarithms.
First, let's start with the given expressions:
1) √x + 1
2) 9 log x
Let's focus on the first expression, √x + 1. We know that the square root (√) can be written as a fractional exponent (1/2). So, we can rewrite the first expression as:
1) (√x)^1/2 + 1
Now, let's use the property of logarithms that states: log(a) + log(b) = log(a * b). Applying this property to the expressions above, we have:
log [ (√x)^1/2 + 1 ]
Next, let's simplify the expression (√x)^1/2. Since the square root (√) cancels out the exponent of 1/2, we are left with:
log ( √x + 1 )
Finally, we have combined the given logarithmic expressions into one log expression:
log ( √x + 1 )
Therefore, the expression can be written as log ( √x + 1 ), where u = √x + 1.