Question 1082035
5^(2p) = 125


take the log of both sides of this equation to get log(5^(2p)) = log(125)


since log(a^b) = b*log(a), this becomes 2p*log(5) = log(125).


divide both sides of this equation by log(5) to get 2p = log(125)/log(5)


solve for 2p to get 2p = 3


solve for p to get p = 1.5


5^2p = 5^3


5^3 = 125


solution looks good


p = 1.5


here's a whole bunch of tutorial on exponents and logs by wtamu that will help you to understand.


<a href = "https://www.google.com/search?q=exponents+wtamu&oq=exponents+wtamu&aqs=chrome.0.69i59.2143j0j4&sourceid=chrome&ie=UTF-8" target = "_blank">https://www.google.com/search?q=exponents+wtamu&oq=exponents+wtamu&aqs=chrome.0.69i59.2143j0j4&sourceid=chrome&ie=UTF-8</a>


<a href = "https://www.google.com/search?q=logarithms+watmu&oq=logarithms+watmu&aqs=chrome..69i57.2415j0j8&sourceid=chrome&ie=UTF-8" target = "_blank">https://www.google.com/search?q=logarithms+watmu&oq=logarithms+watmu&aqs=chrome..69i57.2415j0j8&sourceid=chrome&ie=UTF-8</a>


<a href = "https://www.google.com/search?q=exponential+and+logarithmix+equations+wtamu&oq=exponential+and+logarithmix+equations+wtamu&aqs=chrome..69i57.7087j0j7&sourceid=chrome&ie=UTF-8" target = "_blank">https://www.google.com/search?q=exponential+and+logarithmix+equations+wtamu&oq=exponential+and+logarithmix+equations+wtamu&aqs=chrome..69i57.7087j0j7&sourceid=chrome&ie=UTF-8</a>


all these references come from the main wtamu site which can be found here:


<a href = "http://www.wtamu.edu/academic/anns/mps/math/mathlab/" target = "_blank">http://www.wtamu.edu/academic/anns/mps/math/mathlab/</a>


i have used them in the past and i have learned quite a bit from them.