Question

5^2x = 3(2^x) find x please show steps

Answer 1

Answer:

Step-by-step explanation:

There is a possible issue in your question...

As written it can be interpreted in two ways

like this #1 :

 $5^{2x} = 3(2^x)$

or like this #2 :

  $5^2x = 3(2^x)$

VERSION #1

divide by the 2^x

$\frac{5^{2x} }{2^x} = 3$

to be able to get to the exponent you have to take "logs"

... look up the rules for logs ... log(ab) = log (a)+log(b) , log(a/b) = log(a)-log(b) etc.

if you take the logs of both sides the using the quotient rule and the exponent rule ....result the result is...

$5^{2x}=3\left(2^x\right)\quad :\quad x=\frac{\ln \left(3\right)}{2\ln \left(5\right)-\ln \left(2\right)}\quad \left(\mathrm{Decimal}:\quad x=0.43496\dots \right)$

VERSION #2

$5^2x\:=\:3\left(2^x\right)$

25 x = 3(2^x)

$\frac{25}{3} = \frac{2^{x} }{x}$

This gets really nasty, and I assume that it is not the original problem..

$x=-\frac{\text{W}_{-1}\left(-\frac{3\ln \left(2\right)}{25}\right)}{\ln \left(2\right)},\:x=-\frac{\text{W}_0\left(-\frac{3\ln \left(2\right)}{25}\right)}{\ln \left(2\right)}\quad \mathrm{ }:\quad x=5.52482 ,\:x=0.13144$

Answer 2

Step-by-step explanation:

the answer is in the image above