Theory question 102
Indices and LogarithmsIf 22x−3y = 32 and logyx = 2, find the values of x and y.
Show the model answer
Model answer
22x−3y = 2⁵, so 2x − 3y = 5
logyx = 2 means x = y²
2y² − 3y − 5 = 0, (2y − 5)(y + 1) = 0, y = 5/2 or y = −1
A log base must be positive, so reject y = −1
y = 5/2, x = 25/4
Explanation
Turn the log statement into index form, then substitute.