Exponentials and Logarithms Question

Hi,

I have the answers to the following question but I'm not sure how you work them out:

The loudness of a sound is usually measured in decibels. A decibel is 1/10 of a bel, and a bel represents an increase in loudness by a factor of 10. So a sound of 40 decibels is ten times louder than than a sound of 30 decibels; similarly a sound of 100 decibels is 10 times louder than one of 90 decibels.

(I) Solve the equation x^10 = 10 (I'm fine with this)

(II) Sound A is 35 decibels and sound B is 36 decibels. Show that (to the nearest whole number) B is 26% louder than A. (I've done this, but don't fully understand how the answer works).

(III) How many decibels increase are equivalent to a doubling in loudness? Give your answer to the nearest whole number. (This is the part I need the most help with)

(IIII) Jamie says 'The percentage increase in loudness from 35 to 37 decibels is given by 37-35/35 x 100 = 5.7%'. Explain Jamie's mistake. (I'd appreciate some help here too)

Thank you very much

I would think you're meant to be using the equation from part (I), but it doesn't come across as such from your wording. Can you post an image of the original question, or a link to it?

For ii) what is the equation that relates 1dB to %increase? Similar to i)

is this GCSE or A LEVEL?

Does that mean for every increase of 1dB, no matter what number, the increase is 26%?

Yes,
1dB is a 1.26 multiplier

10dB means a 10 fold increase, irrespective of the value.
1.26^10 = 10

3dB is approximately doubling as
1.26^3 = 2

Yes,
1dB is a 1.26 multiplier

10dB means a 10 fold increase, irrespective of the value.
1.26^10 = 10

3dB is approximately doubling as
1.26^3 = 2

But how did they get that first equation from the information in the q

The thread is 4 years old and its generally best to start a new thread, but which first equation?

If its
x^10 = 10
then its pretty much just given to you, but it represents B being 10 times louder (10 dB) than A
B = 10A
and how this can be reprented in terms of 10 single (1 dB) increases, x, so
B = x*x*....*x*A = x^10 A
So equate and divide by A.