#3**+5 **

Thanks, Bertie.....I see where I made my error (being in too much of a hurry!!)

Let's take it from here.....

log (10)(a^{b}) = log a^{x} by a property of logs, we have

log 10 + log a^{b} = log a^{x} and we have, using another log property

1 + (b) log a = (x) log (a)

(b) log (a) = [ (x) log (a) - 1] divide both sides by log (a)

b = [x - (1 / log (a)) ] ≠ x/10

Thanks again, Bertie, for your sharp eyes!!!....I forgot that the "b" exponent wasn't being applied to the "10" (I hope I got it right this time !!!)

CPhill Apr 24, 2014

#1**0 **

If a^b equals (a^x)/10, will b equal x/10?

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Let's suppose that it's true multiply both sides by 10 we have

10a^{b} = a^{x} take the log of both sides

log 10a^{b} = log a^{x} by a property of logs, we have

b log 10a = x log a and using another log property, we have

b [log 10 + log a] = x log a and because log10 = 1 we have

b [1 + log a] = x log a solving for b, we have

b = [x log a] / [1 + log a] which is definitely ≠ x/10

CPhill Apr 24, 2014

#3**+5 **

Best Answer

Thanks, Bertie.....I see where I made my error (being in too much of a hurry!!)

Let's take it from here.....

log (10)(a^{b}) = log a^{x} by a property of logs, we have

log 10 + log a^{b} = log a^{x} and we have, using another log property

1 + (b) log a = (x) log (a)

(b) log (a) = [ (x) log (a) - 1] divide both sides by log (a)

b = [x - (1 / log (a)) ] ≠ x/10

Thanks again, Bertie, for your sharp eyes!!!....I forgot that the "b" exponent wasn't being applied to the "10" (I hope I got it right this time !!!)

CPhill Apr 24, 2014