Logarithm problem?

Stinkmeaner:

9 ln e² + 4^{log₄6 - log₄2} - 7^{log₇21 + log ₇1}

18lne + 4 ^{log₄ (6/2)} - 7 ^log₇(21*1)

= 18*1 + 3 - 21

= 0
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I never have this too far away when I am dealing with logs

http://en.wikipedia.org/wiki/List_of_logarithmic_identities

9 ln e2 + 4 log (4) 6 - log (4) 2 - 7 log (7) 21 + log (7) 1

SOLUTION:

9 ln (e^2) = 18 ln e = 18, since in e = 1

4 log (4) 6 - log (4) 2 = log (4) 6^4 - log (4) 2 = log (4) 6^4/2 = log (4) 648

In base 10, log (4) 648 = log 648/ log 4 = 4.67 (2dcpl)

Log 1 = 0, for any base.

So that 7 log (7) 21 in base 10 = 7 log 21/log 7 = 10.95 (2dcpl)

Hence, we have

18 + 4.67 - 10.95 = 11.72

ALTERNATIVELY,

9 ln e2 + 4 log (4) 6 - log (4) 2 - 7 log (7) 21 + log (7) 1

Converting everything to base 10 at once and working thenceforth,

18 ln e + (4 log 6/log 4) - (log 2/log 4) - (7 log 21/ log 7) + (log 1/ log 7)

18 + 4.67 + 10.95 + 0 = 11.72.

Stinkmeaner:

9 ln e² + 4^{log₄6 - log₄2} - 7^{log₇21 + log ₇1}

Hi Demogorgon,

You and I have interpreted this question differently from one another.

9 ln e ² +4 ^{log₄6 - log₄2} - 7 ^{log₇21 + log ₇1}

I interpreted this as
9 ln e ² +4 ^ [log ₄6 - log ₄2 ] - 7^ [ log ₇21 + log ₇1 ]

9 ln e ² +4^ [ log ₄ (6/2) ] - 7^ [ log ₇(21*1) ]

......
= 0 As I found before.

You have treated them as multiply instead of to the power of.
I think that I am correct.
(I am happy for someone else to arbitrate though )