Answer:
3 log (z) - 1/2log (x) - 1/2 log (5) -1/2 log y
Step-by-step explanation:
log(z3)/√x5y)
= log (z3) - log (√x5y) [division being subtracted]
= 3 log (z) - {log (√x) + log (√5y)} [ multiplication being added in the denominator]
= 3 log (z) - {log (x)^1/2 + log (5)^1/2+ log (y)^1/2}
= 3 log (z) - 1/2{log (x) + log (5)+ log y }
We can solve inside the curly bracket and then multiply with 1/2 or we can solve it separately
= 3 log (z) - 1/2log (x) - 1/2 log (5) -1/2 log y
How does this work?
1) any two terms being multiplied in logarithms are added with the log of each.
2) the exponent becomes the co- efficient.
3) any two terms being divided in logarithms are subtracted with the log of each
