Question Details

If 92x-1-81x-1=1944, then x is

Options

A

3

B

9/4

C

4/9

D

1/3

Show Answer

Correct Answer :

Option B

9/4

Solution :

The correct option is B (which corresponds to 9/4).

Given equation:
92x-1-81x-1=1944

We can write 81 as 92:
81x-1=(92)x-1=92x-2

Now substitute this back into the equation:
92x-1-92x-2=1944

Factor out the common term 92x-2:
92x-2(91-1)=1944
92x-2(8)=1944

Divide both sides by 8:
92x-2=19448
92x-2=243

Express both 9 and 243 as powers of 3 (since 9=32 and 243=35):
(32)2x-2=35
34x-4=35

Since the bases are equal, equate the exponents:
4x-4=5
4x=9
x=94

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