Answer:
x=6
Step-by-step explanation:
81^x = 27 ^(x+2)
81 = 3^4 and 27 =3^3 so replace 81 and 27 in the equation
3^4^x = 3^3^(x+2)
When we have a power to a power we can multiply the exponents
a ^b^c = a^(b*c)
3^(4x) = 3^(3*(x+2))
Since the bases are the same, the exponents have to be the same
a^b = a^c means b=c
4x = 3(x+2)
Now we can solve for x
Distribute
4x = 3x+6
Subtract 3x from each side
4x-3x = 3x-3x+6
x = 6
It’s an irrational number. 3.08007288, just round it to the nearest whole number and you’ll get 3.
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