log10^x = 2a and log10^y = b/2 write If log 10^p = 3a-2b, express p in terms of x and y

Question

I have not solved the question. But this is required for learning of my daughter

Answer 1

Note:  I'm assuming log10^x = 2a means log(10^x) = 2a.  If that is wrong, then the answer below would be wrong.

Note:  log(10) = 1

 

log(10^x) = 2a

x*log(10) = 2a

x = 2a

a = x/2

 

log(10^y) = b/2

y*log(10) = b/2

y = b/2

b = 2y

 

log(10^p) = 3a - 2b

p*log(10) = 3a - 2b

p = 3a - 2b

p = 3(x/2) - 2(2y)

p = (3/2)x - 4y