Question

Решить уравнение (1/3)^x-7=3

Answer 1

Ответ:

6

Пошаговое объяснение:

$\frac{1}{3} ^{x-7} = \frac{1}{3}^{-1}$

Т.к. основания равны, то и степени должны быть равны.

Т.е. х-7 = -1, х = 7-1, х=6

Answer 2

To solve the equation $(\frac{1}{3})^x - 7 = 3$, we need to isolate the variable $x$. Let's go step by step:

Step 1: Add 7 to both sides of the equation to eliminate the constant term on the left side: $(\frac{1}{3})^x = 3 + 7 = 10$.

Step 2: Now, we have an equation with a base of $\frac{1}{3}$. To eliminate the exponent, we can take the logarithm of both sides. The choice of the logarithm base is not critical, but we'll use the natural logarithm (ln) for simplicity:

$ln((\frac{1}{3})^x) = ln(10).$

Step 3: Apply the logarithm property $ln(a^b) = b * ln(a)$ to bring down the exponent:

$x * ln(\frac{1}{3}) = ln(10).$

Step 4: Finally, solve for $x$ by dividing both sides by $ln(\frac{1}{3})$:

$x = \frac{ln(10)}{ln(\frac{1}{3})}.$

Now, let's calculate the numerical value of $x$:

$x = \frac{ln(10)}{ln(\frac{1}{3})} \approx -6.192.$

So, the solution to the equation is approximately $x \approx -6.192$.