CAT Practice : Exponents and Logarithms

Basic Identities of Logarithms

Basic identities of Logarithm

Q.12: 10log(3 - 10logy) = log2(9 - 2y), Solve for y
1. 0
2. 3
3. 0 and 3
4. none of these

Choice D. none of these

Detailed Solution

Before beginning to simplify the equation, don’t forget that anything inside a log cannot be negative

10log(3-y) = log2(9 - 2y) (y>0)…………………………………(1)

3 - y = log2(9 - 2y) (3-y>0 =) (y<3)………………….. (2)

23-y = 9 - 2y

2y = t

$\frac{2^3}{t} = 9 - t$

=) 8 = 9t –t2

=) t2-9t+8 = 0

=) t2-t-8t-8 = 0

=) t(t-1)-8(t-1) = 0

=) t = 1,8

Therefore, 2y = 1 and 2y = 8

=) y = 0 =) y = 3

However, from inequalities (1) and (2), y cannot take either of these value So

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