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Dear Mr. Wilson I'm a bit stuck in solving these equations. Could you please help me? Thank you so much

It should be noted that log(a^x) = x*log(a) and that log(c) + log(d) = log(cd).

These two can be combined to note that log(e) - log(f) = log(e/f).

Note that 4 is the log(10,000).

Using the preceeding comments, we can rewrite equation 1 as

logA = logx + log√B - logC - log(10,000).

We can then say that logx = logA - log√B + logC + log(10,000).

Since we have all terms as a log, we can rewrite it as logx = log(10,000*A*C/B).

It is then known that x = 10,000*A*C/B.

The 2nd equation can be rewritten as loga(√x^6) - loga(x^2) = loga(3/x^2).

Since √x^6 = x^3, we have loga(x³) - loga(x²) = loga(3/x²).

Since we have the difference of logs, this can be transformed to loga(x³/x²) = loga(3/x²).

Since x³/x² = x, this is the same as loga(x) = loga(3/x²).

We can drop that loga on both sides, giving x = 3/x².

Multiplying both sides by x² gives x³ = 3.

Taking the cuberoot of both sides gives x = 3^(1/3).

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