Log question: If a = b^c and x=a^d ..... then show that logbx = logba.logax

woodburyboy

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Here's one presented to me by my daughter studying Civil Engineering at Cardiff that I just cant work out. Any help much appreciated:

If a = b^c and x=a^d ..... then show that logbx = logba.logax
 
Here's one presented to me by my daughter studying Civil Engineering at Cardiff that I just cant work out. Any help much appreciated:

If a = b^c and x=a^d ..... then show that logbx = logba.logax
Hello. I'm not sure about that part. Is your daughter asking for assistance? Or, maybe she presented this as a challenge for you? (It's high-school algebra.)

This exercise deals with (1) definitions of logarithm, base, exponent, (2) some basic properties of logarithms and exponents, and (3) the change-of-base formula.

It's about using what's been learned of (1), (2), and (3), to make substitutions as needed, solving for certain symbols, and using the change-of-base formula -- all to achieve the requested equation. There's probably more than one way to do it.

What's been tried so far? Please share any work (even if you're not sure it's correct), so we have some idea where to begin helping. :cool:
 
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