Question

49^x-3= 7^x pleaseeeeeee

Answer 1

49=7^2
2(х-3)=х
2х-6=х
х=6
49^3=7^6
7^6=7^6

Answer 2

To solve the equation 49^x - 3 = 7^x, we can use logarithms. Taking the logarithm of both sides of the equation will help us simplify it and solve for x.

Step 1: Take the logarithm of both sides

We can take the logarithm of both sides of the equation using any base. Let's use the natural logarithm (base e) for this example.

Taking the natural logarithm of both sides, we get:

ln(49^x - 3) = ln(7^x)

Step 2: Apply logarithmic properties

Using the logarithmic property ln(a^b) = b * ln(a), we can simplify the equation further:

x * ln(49) - ln(3) = x * ln(7)

Step 3: Rearrange the equation

To solve for x, we need to isolate the x terms on one side of the equation. Let's rearrange the equation:

x * ln(49) - x * ln(7) = ln(3)

Step 4: Factor out x

We can factor out x from the left side of the equation:

x * (ln(49) - ln(7)) = ln(3)

Step 5: Solve for x

To solve for x, divide both sides of the equation by (ln(49) - ln(7)):

x = ln(3) / (ln(49) - ln(7))

Now, let's calculate the value of x using the given equation.

Using the natural logarithm function, we can calculate ln(3), ln(49), and ln(7).

ln(3) ≈ 1.0986 ln(49) ≈ 3.8918 ln(7) ≈ 1.9459 Substituting these values into the equation, we get:

x ≈ 1.0986 / (3.8918 - 1.9459)

Calculating the expression on the right side, we find:

x ≈ 1.0986 / 1.9459 ≈ 0.5644

Therefore, the approximate value of x that satisfies the equation 49^x - 3 = 7^x is x ≈ 0.5644.

Please note that this is an approximate solution, and the actual value of x may vary depending on the level of precision required.