for what values of x is log0.75(x+3) > log0.5(x+3)

To solve the inequality \( \log_{0.75}(x + 3) > \log_{0.5}(x + 3) \), we can first convert the logarithms to the same base, or we can analyze the properties of the logarithmic functions involved.

1. **Understanding the log properties**:
The base 0.75 logarithm is decreasing because 0.75 is less than 1, while the base 0.5 logarithm is also decreasing for the same reason. Thus, for any valid input \( x + 3 > 0 \), we can compare \( x + 3 \) directly.

2. **Reformulating the inequality**:
Since both logarithms are decreasing functions, we can reverse the inequality when we take the argument of the logarithms:

\[
x + 3 < (x + 3)
\]

However, this does not hold because we're comparing two functions rather than two quantities being directly compared.

3. **Using the change of base**:
We can express the logarithm conversion:

\[
\log_{0.75}(x + 3) = \frac{\log(x + 3)}{\log(0.75)}
\]
\[
\log_{0.5}(x + 3) = \frac{\log(x + 3)}{\log(0.5)}
\]

Thus, our inequality becomes:

\[
\frac{\log(x + 3)}{\log(0.75)} > \frac{\log(x + 3)}{\log(0.5)}
\]

Since \( \log(0.75) < 0 \) and \( \log(0.5) < 0 \), we multiply both sides by the negative \( \log(0.75) \) (which flips the inequality):

\[
\log(x + 3) < \log(x + 3) \cdot \frac{\log(0.5)}{\log(0.75)}
\]

4. **Finding the condition**:
Recall that an inequality of logarithmic forms indicates the relationship of the arguments. We need to validate:

\[
(x + 3)^{\frac{\log(0.75)}{\log(0.5)}} < 1
\]

5. **Determine when this occurs**:
Since \(\log(0.75) < 0\) and \(\log(0.5) < 0\),

\[
\frac{\log(0.75)}{\log(0.5)} > 1
\]

Meaning:

\[
x + 3 < 1
\]
Simplifying gives:

\[
x < -2
\]

6. **Consider constraints**:
Since the logarithmic function is defined for positive arguments, we must also have:

\[
x + 3 > 0 \implies x > -3
\]

7. **Final interval**:
Now, we need to satisfy both conditions: \(x < -2\) and \(x > -3\). The solution is the interval:

\[
-3 < x < -2
\]

So, the solution for the inequality \( \log_{0.75}(x + 3) > \log_{0.5}(x + 3) \) is:

\[
\boxed{(-3, -2)}
\]