Question

уравнение 9^x-6=3^x

Answer 1

$3^{2x}$-$3^{x}$-6=0
$3^{x}$=t
$t^{2}$-t-6=0
D=1+24=25
отрицательное значение t нам не подойдет, тогда:
t=$\frac{1+5}{2}$=3
$3^{x}$=3
x=1

Answer 2

I can help you solve the equation $9^x-6=3^x$ in detail. Here are the steps:

1. Rewrite the equation as $3^{2x}-6=3^x$ by using the property $a^b=a^{b\cdot 1}=a^{b\cdot c^0}=(a^c)^{b\cdot 0}=(a^c)^b$ with $a=3$, $b=x$, and $c=2$. 2. Take the natural logarithm of both sides: $\ln(3^{2x}-6)=\ln(3^x)$. 3. Use the logarithm power rule to move the exponents to the front: $2x\ln(3)-\ln(6)=x\ln(3)$. 4. Isolate $x$ by subtracting $x\ln(3)$ from both sides and dividing by $\ln(3)$: $x=\frac{\ln(6)}{\ln(3)}$. 5. Simplify the expression using a calculator: $x\approx 1.63093$.

The solution is $x\approx 1.63093$. You can check your answer by plugging it into the original equation and verifying that both sides are equal.

You can also use an online equation solver to get the same result. Alternatively, you can use an algebraic calculator or a math solver to solve other types of equations.

I hope this helps. If you have any other questions, feel free to ask me.