How many roots are there to $x=8^{\log_2x} -9^{\log_3x}-4^{\log_2x}+\log_{0.5}{0.25}$?

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The number of positive values \(x\) which satisfy the equation \[x=8^{\log_2x} -9^{\log_3x}-4^{\log_2x}+\log_{0.5}{0.25}\] is

1. 0;

2. 1;

3. 2;

4. 3.

Can we evaluate \(\log_{0.5}{0.25}\) ?

We know that \(8\) is a power of \(2\) – could use this fact to rewrite \(8^{\log_2x}\)?