(ii) Solve log, (5y + 40) – log, (+2) = 2.
Answers
Step-by-step explanation:
Simplifying
log[5](5y + 40) + -1log[5](y + 2) = 2
Reorder the terms:
glo * 5(40 + 5y) + -1log[5](y + 2) = 2
Reorder the terms for easier multiplication:
5glo(40 + 5y) + -1log[5](y + 2) = 2
(40 * 5glo + 5y * 5glo) + -1log[5](y + 2) = 2
(200glo + 25gloy) + -1log[5](y + 2) = 2
Reorder the terms:
200glo + 25gloy + -1glo * 5(2 + y) = 2
Reorder the terms for easier multiplication:
200glo + 25gloy + -1 * 5glo(2 + y) = 2
Multiply -1 * 5
200glo + 25gloy + -5glo(2 + y) = 2
200glo + 25gloy + (2 * -5glo + y * -5glo) = 2
200glo + 25gloy + (-10glo + -5gloy) = 2
Reorder the terms:
200glo + -10glo + 25gloy + -5gloy = 2
Combine like terms: 200glo + -10glo = 190glo
190glo + 25gloy + -5gloy = 2
Combine like terms: 25gloy + -5gloy = 20gloy
190glo + 20gloy = 2
Solving
190glo + 20gloy = 2
Solving for variable 'g'.
Move all terms containing g to the left, all other terms to the right.
Reorder the terms:
-2 + 190glo + 20gloy = 2 + -2
Combine like terms: 2 + -2 = 0
-2 + 190glo + 20gloy = 0
Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 95glo + 10gloy) = 0
Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 95glo + 10gloy)' equal to zero and attempt to solve:
Simplifying
-1 + 95glo + 10gloy = 0
Solving
-1 + 95glo + 10gloy = 0
Move all terms containing g to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 95glo + 1 + 10gloy = 0 + 1
Reorder the terms:
-1 + 1 + 95glo + 10gloy = 0 + 1
Combine like terms: -1 + 1 = 0
0 + 95glo + 10gloy = 0 + 1
95glo + 10gloy = 0 + 1
Combine like terms: 0 + 1 = 1
95glo + 10gloy = 1
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.
The solution to this equation could not be determined.