So I have to an expression as the logarithm of a single number or expression with a coefficient of 1
9log w+ 4log z- log(x-5)
my answer is: log w^4*z^9/(x-5).. is this right?
thanks in advance!
You put the exponents on the wrong variables,
I get
log ((w^9 z^4)/x-5))
Log6+log3
To simplify the expression 9log w + 4log z - log(x-5), we can use the properties of logarithms:
1. The power property: log base a of (x^y) = y * log base a of x
2. The product property: log base a of (xy) = log base a of x + log base a of y
3. The quotient property: log base a of (x/y) = log base a of x - log base a of y
Let's apply these properties step by step:
Step 1: Apply the power property to simplify 9log w:
9log w = log w^9
Step 2: Simplify 4log z:
4log z = log z^4
Step 3: Simplify -log(x-5):
-log(x-5) = log (x-5)^(-1)
Now, let's combine the above simplifications using the product and quotient properties:
log w^9 + log z^4 - log (x-5)^(-1)
Using the product property on log w^9 and log z^4, we get:
log (w^9 * z^4) - log (x-5)^(-1)
Now, let's apply the quotient property to subtract the log (x-5) term:
log [(w^9 * z^4) / (x-5)^(-1)]
Finally, applying the power property again to bring the denominator inside the log, we get:
log [(w^9 * z^4) * (x-5)]
Thus, the simplified expression is:
log (w^9 * z^4 * (x-5))
So, your answer: log (w^9 * z^4 * (x-5)) is correct.