Theory question 101
Indices(a) Given that 3 × 91+x = 27-x, find x.
(b) Evaluate log10√35 + log10√2 − log10√7.
Show the model answer
Model answer
(a) Write everything as powers of 3: 3 × 32(1+x) = 3-3x
So 1 + 2 + 2x = −3x, 5x = −3, x = −3/5
(b) Combine: log10(√35 × √2 ÷ √7) = log10√10
= ½ log1010 = ½
Explanation
Use a common base for indices, and the product/quotient laws for logs.