Logarithms

[dinosaur93]

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 where is the loudness of the sound (dB) and is the intensity of the sound.

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


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


Q3
A student solves for in the equation log₂₇ (81a)=b. PROVE that the student determines a equivalent to the expression a=3^3b-4

[REBORN]

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

[monkeywantsabanana]

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

[dinosaur93]

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!