24 7e2X 28e6xSolution7e2x 28e6x 7e2x 28e6x since an 1an

24. 7e^2X = 28e^-6x

7e^2x = 28e^-6x

==> 7e^2x = 28/e^6x since a^-n = 1/aⁿ

==> e^6x e^2x = 28/7

==> e^{6x +2x} = 4 since a^m aⁿ = a^m+n

==> e^8x = 4

Apply natural logarithm on both sides

==> ln e^8x = ln4

==> 8x lne = ln4 since lna^b = b lna

==> 8x(1) = ln4

==> x = (1/8) ln4

==> x = (1/8) ln 2²

==> x = (1/8)(2) ln2

==> x = (1/4) ln2

==> x = (1/4) (0.69315)

==> x = 0.1733

Hence x = 0.1733