Question

Can someone help me with these two questions about Logarithms? If you can, please don't just tell me the answer. I really want to understand how to do these so please add an explanation. Please and thank you. ^^

My phone wouldn't let me send the photos so here are the questions:

1. The loudness, L, of a sound in decibels is given by L=10logR, where R is the sound's relative intensity. if the intensity of a certain sound is tripled, by how many decibels does the sound increase?

2. An earthquake rated at 3.5 on the Richter scale is felt by many people and an earthquake rated at 4.5 may cause local damage. The Richter scale magnitude reading, m, is given by m=logx, where x represents the amplitude of the seismic wave causing ground motion. How many times greater is the amplitude of an earthquake that measures 4.5 than one that measures 3.5?

Answer 1

1.
plug in numbers so use R=1500 and 3R=1500(3)
so you get 36.53-31.76=about 4.77
2.
so put put 4.5 in the formula and 3.5 in the formula and divide them
4.5=logx
10^4.5=x
then 3.5=logx
10^3.5=x
(10^4.5)/(10^3.5)
= 10