resolve the following exponential equation

3 ^ (x + 4) = 5 ^ (x + 2)

you question doesn't make much sense.

how can (x + 4) be the exponent from the base of 3?

(x+4) log 3 = (x+2) log 5

(x+4)/(x+2) = log 5/log 3 = 1.46497
x + 4 = 1.46497 x + 2.92995
0.46497 x = 1.07005
x = 2.3013..

There is nothing wrong with the question. Ignore Hannie's comment.

(x+4)log3 = (x+2)log5

(x+4)(0.47712) = (x+2)(0.69897)
0.47712x + 1.90848 = 0.69897x + 1.39794
0.22185x = 0.51054
x=2.301

Checking you will probably find a small rounding error. If you carry the calculations to a lot of decimal places it will be more exact.

thanks so much! i was sure it had logs involved but wasn't sure. thanks drwls and quidditch!

To solve the exponential equation 3^(x + 4) = 5^(x + 2), we can take the logarithm of both sides of the equation. By doing so, we can use the properties of logarithms to simplify the equation and find the value of x.

Here's the step-by-step process:

Step 1: Take the logarithm of both sides
log(3^(x + 4)) = log(5^(x + 2))

Step 2: Apply the exponent rule of logarithms (log base a of b^c = c * log base a of b) to the left side of the equation:
(x + 4) * log3 = (x + 2) * log5

Step 3: Distribute on both sides:
x * log3 + 4 * log3 = x * log5 + 2 * log5

Step 4: Move all terms with x to one side of the equation:
x * log3 - x * log5 = 2 * log5 - 4 * log3

Step 5: Factor out x from the left side:
x * (log3 - log5) = 2 * log5 - 4 * log3

Step 6: Divide both sides of the equation by (log3 - log5) to solve for x:
x = (2 * log5 - 4 * log3) / (log3 - log5)

Now you can calculate the value of x using the logarithmic properties and the values of log3 and log5.