Löse die Gleichung ohne Taschenrechner: 8·√(9^x) = 3^{7x+10} + 5·3^x

Question

Löse die Gleichung ohne Taschenrechner:

$$8*\sqrt { { 9 }^{ x } } =\quad { 3 }^{ 7x+10 }+5*{ 3 }^{ x }$$

Answer 1

                                             

Answer 2

8*sqrt(9^x)=8*3^x=3^{7x+10}+5*3^x

3*3^x=3^{7x+10}

3^{x+1}=3^{7x+10}

x+1=7x+10

x=-3/2

Answer 3

8·9^{x/2} = 3^{7·x + 10} + 5·3^x

8·3^x = 3^{7·x + 10} + 5·3^x

3·3^x = 3^{7·x + 10}

3^{x + 1} = 3^{7·x + 10}

x + 1 = 7·x + 10

6·x = - 9

x = -9/6 = -3/2 = -1.5