Question

Lösen Sie: 3*4^{x+1}=5*6^{x/2}

Answer 1

Hi,

3*4^{x+1} = 5*6^{x/2}

12*4^x = 5*6^{x/2}   |:4^x :5

12/5 = 6^{x/2}/4^x    |ln

ln(12/5) = ln(6^{x/2}/4^x)  |ln(a/b) = ln(a)-ln(b)

ln(12/5) = ln(6^{x/2}) - ln(4^x)   |ln(a^n) = n*ln(a)

ln(12/5) = x/2*ln(6) - x*ln(4)

x(1/2*ln(6) - ln(4)) = ln(12/5)

x = ln(12/5) / (1/2*ln(6) - ln(4)) ≈ -1,785


Grüße

Comments

wie komm ich denn von 3*4^{x+1} auf 12*4^x ?

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Es ist 4^{x+1} = 4^x*4, denn a^n*a^m = a^{n+m}


;)

Answer 2

3·4^{x + 1} = 5·6^{x/2}

12·4^{x} = 5·6^{x/2}

12·16^{x/2} = 5·6^{x/2}

(16/6)^{x/2} = 5/12

x = LN(5/12) / LN(16/6) * 2 = -1.785160331