Sec 3 Maths

Solve for x

(4^(3x))(x+1)=8(x+1)^(2x)

There is a typo error earlier and the error is corrected.

Hi,

1. Simplify, by applying rules of indices, till you obtain

8^(2x - 1) = (x + 1)^(2x - 1).

2. Take log (or natural) of both sides, from which one of the answers (1/2) would be obvious.

Thanks.

Cheers,
Wen Shih

Hi,

1. Simplify, by applying rules of indices, till you obtain

4^(2x - 1) = (x + 1)^(2x - 1).

2. Take log (or natural) of both sides, from which the answer (1/2) will be obvious.

Thanks.

Cheers,
Wen Shih

The answer of 1/2 does not seem to be correct both before and after the typo error is corrected.

Hi,

Starting with 8^(2x -1) = (x + 1)^(2x - 1)

=> (2x - 1) ln 8 = (2x - 1) ln (x + 1)

=> (2x - 1) ln (8/(x + 1)) = 0

=> 2x - 1 = 0 or 8/(x + 1) = 1

=> x = 1/2 or x = 7.

Thanks.

Cheers,
Wen Shih

Hi,

Let's verify, when x = 1/2:

LHS = (4^1.5)(1.5) = 12

RHS = 8(1.5) = 12.

Thanks.

Cheers,
Wen Shih

Thanks. The answer 1/2 is indeed correct. My bad for not verifying your answer.

However, the answer x = 7 is also another possible answer.

(4^(3x))(x+1)=8(x+1)^(2x)

(4^21)(8)= 8(8^14)

2^42=2^42

Strange, why is that there are two possible answers ?