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Solve for x:(a) log(0.3)(x^(2)+8) gt log...

Solve for `x:(a) log_(0.3)(x^(2)+8) gt log_(0.3)(9x)`, b) `log_(7)( (2x-6)/(2x-1)) gt 0`

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Let's solve the given inequalities step by step. ### Part (a): Solve for \( x \) in the inequality \( \log_{0.3}(x^2 + 8) > \log_{0.3}(9x) \) 1. **Identify the base of the logarithm**: The base is \( 0.3 \), which is less than 1. This means that the logarithmic function is decreasing. 2. **Apply the properties of logarithms**: Since the logarithm is decreasing, we can reverse the inequality when we take the antilog of both sides: \[ ...
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