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27^{(2x - 1)} = 243^{3}

We can express both sides in terms of 3.

27 = 3^{3}

243 = 3^{5}

Hence, the equation becomes:

3^{3(2x - 1)} = 3^{5(3)}

3^{6x - 3} = 3^{15}

from indices, since both sides have same number. i.e 3, we just evaluate the power. That is,

6x - 3 = 15

add 3 to both sides,

6x - 3 + 3 = 15 + 3

6x = 18

divide both sides by 6

x = 18/6

x = 3

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