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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: dinosaur93 on November 01, 2011, 03:05:20 pm

Title: Logarithms
Post by: dinosaur93 on November 01, 2011, 03:05:20 pm: Guys, kindly help me figure out this Qs by hand!!! tnx in advance!

The decibel level of a sound may be calculated using the formula $L=10log(10^1^2*I)$ where $L$ is the loudness of the sound (dB) and $I$ is the intensity of the sound.

Q1
An equation that can be used to solve for the value of $I$ is _____?_____

Q2
The loudness of a jet engine is 150 dB, The magnitude of the sound intensity is _____?_____

Q3
A student solves for $a$ in the equation log₂₇ (81a)=b. PROVE that the student determines a equivalent to the expression a=3^3b-4
Title: Re: Logarithms
Post by: REBORN on November 01, 2011, 03:07:27 pm: Q3 - convert to exponential form.

27^b = 81a

a = 27^b divided by 81

27 is the same as 3 cubed. 81 is the same as three quadrubed. (^4)

Thus 3^3b divided by 3^4 is the same as 3^3b-4
Title: Re: Logarithms
Post by: monkeywantsabanana on November 01, 2011, 06:09:33 pm: Sorry, I don't know how to use LATEX but here:

Q1

L=10log₁₀(10^12 x I)
L/10= log₁₀(10^12 x I)
10^(L/10) = 10^12 x I
10^(L/10) / 10^12 = I
10^(L/10)-12 = I
10^(L-120/10) = I

Q2

150=10log₁₀(10^12 x I)
15=log₁₀(10^12 x I)
10^15=10^12 x I
10^15/10^12=I
I= 10^3

Hope I didn't make any mistakes
Title: Re: Logarithms
Post by: dinosaur93 on November 01, 2011, 07:06:36 pm: dude, Wehn I was doing the questions, I get the part where you solve from
L=10log10(10^12 x I)
L/10= log10(10^12 x I)

but eventually didn't get how to derive to
10^(L/10) = 10^12 x I

lol, thats alright mate, tnx heaps!