How do you solve 243.2x=81x+5?

1 Answer

x=203

Explanation:

243.2x=81x+5

Simplifying the bases by prime factorisation:

243=33333=35

81=3333=34

Thus, using the rule (ab)c=a(bc):

243,2x=3(5×.2x)=3x

81x+5=3(4(x+5))=34x+20

The expression becomes:

3x=34x+20

The bases are equal so we can equate powers:

x=4x+20

x4x=20

3x=20

x=203