two questions about logs in Math - I know the answers but not the process

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Doctor Bob

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two questions about logs in Math - I know the answers but not the process

I know the answers to the following two problems re logs but I don\'t know the procedure.
Please explain steps. Thank you.

log sub 3 (81)^-2.3= -9.2 (Why?)

sq rt 2
log sub 2 ------- = - 5/2 (Why?)
8

Posted 199 day ago

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Answers (6)

atta

logBase3Of(81)^(-2.3) = -9.2. By using the rules and properties of logarithms such as logu^n = nlogu thereby requiring the following equality:
logBase3Of(81)^-2.3 = -9.2 => -2.3logBase3Of(81) = -9.2 => logBase3Of(81) 9.2/2.3 = 46/5 / 23/10 = 460/115 = logBase3Of(3)^4 = log81 / log3 = 4 => logu / logv = log(u/v) thus yielding log81/log3 = log(81/3) = log 27 = log(3)^3 = 4 => 3log3 = 4 => log3 = 0.75 thus yielding 10^log3 = 10^0.75 => -5.2

Posted 194 day ago

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Amar Soni

PLEASE SEND YOUR E-MAIL ADDRESS I WILL SEND YOUR REPLY IN DETAIL.

Posted 198 day ago

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matherapist

The key to all the answers given is applying the rules of exponents. for this problem you are using a number raised to a power raised to a power (a^c)^d = a^(cd)

Posted 198 day ago

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YummyCookies

Let log base3 81^-2.3 = X

then 81^-2.3 = 3^x

but since 81^1/4 = 3

then: 3^x = 81^x/4

so: 81^-2.3 = 81^x/4

thus, -2.3 = x/4

solving for x gives x = -9.2

Posted 198 day ago

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your second problem is not printed correctly, must be typed again. But the answer to your first problem is shown below:

Let log(base 3) (81)^-2.3 = x, therefore:
3^x = (81)^(-2.3), eq(1), but:
(3)^4 = 81, so:
(81)^(-2.3) = [(3)^4]^(-2.3)= 3^(-9.2).
Replace this in eq(1), we get:
3^x = 3^(-9.2) which means :
x = -9.2.<==== Answer

Posted 199 day ago

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MFB13

Hi. I was not sure how you exactly wrote your second example but since I was able to read your first example clearly, I can show you the process in the first example.

Let log base3 81^-2.3 = X

then 81^-2.3 = 3^x

but since 81^1/4 = 3

then: 3^x = 81^x/4

so: 81^-2.3 = 81^x/4

thus, -2.3 = x/4

solving for x gives x = -9.2

I wasn't sure how you wrote your second example otherwise I should be able to go thru that example as well.

Posted 199 day ago

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