# Find X

27^4x-2=243^3x=6

Please Explain

Thanks

Is this a repeat of the problem you posted earlier? If so, it should be

**27 ^{4x-2} = 243^{3x+6} **Post your work if you get stuck.

You might try it the hard way.

(4x-2)*log 27 = (3x+6)*log (243)

Solve for x. I get -12.

You have too many = signs. Is the second one (before the 6) supposed to be a + or - ? Is the first exponent supposed to be x-2 or x ?

You need to learn how to use parentheses to clarify your equations when typing them.

## Apologies for the confusion earlier. Let's clarify the equation and solve for x.

The corrected equation is:

27^(4x-2) = 243^(3x+6)

To solve for x, we can take the logarithm of both sides of the equation. We can use any base for the logarithm, but let's choose the common logarithm (base 10) for this explanation.

Applying the logarithm to both sides:

log(27^(4x-2)) = log(243^(3x+6))

Using the logarithmic property that log(a^b) = b * log(a):

(4x - 2) * log(27) = (3x + 6) * log(243)

To evaluate this equation, we need to know the values of log(27) and log(243).

Using the calculator, we find:

log(27) ≈ 1.431

log(243) ≈ 2.385

Now, let's substitute these values back into the equation:

(4x - 2) * 1.431 = (3x + 6) * 2.385

Now, we can solve for x by simplifying and isolating the variable:

1.431 * 4x - 1.431 * 2 = 2.385 * 3x + 2.385 * 6

5.724x - 2.862 = 7.155x + 14.31

Moving the variables to one side and the constants to the other side:

5.724x - 7.155x = 14.31 + 2.862

-1.431x = 17.172

Dividing both sides by -1.431 to solve for x:

x = 17.172 / -1.431

Calculating this expression, we find:

x ≈ -11.99

Therefore, the approximate value of x is -11.99.

Keep in mind that, in mathematics, it is common to round decimal values for simplicity. The exact value of x in the equation might be an infinitely repeating decimal.