I think you have taken the log with base 10. The answer 1/12 is obtained when 'e' is used as the base. Perhaps you have done it correct otherwise. I am giving here another approach of solution:
Rewrite the given equation as
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Solve for exact value of x for (3x)^lg3 = (4x)^lg 4
[Ans = 1/12]
I took lg on both sides and rearranged to get
lg 3x / lg 4x = lg 4 / lg 3
lg 3x / lg 4x = 1.262 (evaluate)
lg 3x = 1.262 lg 4x (Cross-multiply)
lg 3x - lg 4x^1.262 = 0
lg (3x/4x^1.262) = 10^0
3x = 4x^1.262
3/4 = x^1.262 / x
Solving, x = 3/4^(1/0.262) = 0.334
Please advise where I went wrong with my working, coz my answers' not right!
Thanks !
Hello, Drdj!
If we are very careful, we can solve it without a calculator.
Take logs (base 10): .
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. . = . . .
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. . . . . . . . . . . . . . . . . . . .
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. . . . . . . . . . . .Therefore: . . .