Question

3*7^(x+1)*5*7^(x-1)=152

Answer 1

Ответ:

Пошаговое объяснение:

Сорян нужны баллы

Answer 2

To solve the equation 3 * 7^(x+1) * 5 * 7^(x-1) = 152, we can simplify it step by step:

1. Start by simplifying the left side of the equation:

   3 * 7^(x+1) * 5 * 7^(x-1) = 15 * 7^(x+1) * 7^(x-1)

2. Now, use the properties of exponents to combine the two 7 terms with the same base:

   15 * 7^(x+1) * 7^(x-1) = 15 * 7^(x+1+x-1)

3. Combine the exponents:

   15 * 7^(2x) = 15 * 49^x

4. Now the equation looks like:

   15 * 49^x = 152

5. Divide both sides of the equation by 15 to isolate the term with the exponent:

   49^x = 152 / 15

6. Calculate the right side:

   49^x ≈ 10.1333

7. To solve for x, take the logarithm of both sides. You can use the natural logarithm (ln) or the common logarithm (log base 10). Let's use the natural logarithm:

   ln(49^x) = ln(10.1333)

8. Use the properties of logarithms to bring the exponent down:

   x * ln(49) = ln(10.1333)

9. Divide both sides by ln(49) to solve for x:

   x = ln(10.1333) / ln(49)

10. Use a calculator to compute the values of ln(10.1333) and ln(49):

x ≈ 0.3273 / 3.8918

11. Finally, calculate the value of x:

x ≈ 0.0839

So, the approximate value of x that solves the equation is x ≈ 0.0839.