2^x+2^(x-1)+2^(x-2)=7^x+7^(x-1)+7^(x-2) The number of solutions for x are:
P.s.- if anyone solves it, can you please show how and what are the solutions?
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2 x + 2 x − 1 + 2 x − 2 = 7 x + 7 x − 1 + 7 x − 2
2 x ⋅ ( 1 + 2 1 + 4 1 ) = 7 x ⋅ ( 1 + 7 1 + 4 9 1 )
2 x ⋅ ( 4 7 ) = 7 x ⋅ ( 4 9 5 7 )
4 × 5 7 7 × 4 9 = 2 x 7 x
2 2 8 3 4 3 = ( 2 7 ) x
lo g 3 4 3 − lo g 2 2 8 = lo g ( 7 x ) − lo g ( 2 x )
lo g 3 4 3 − lo g 2 2 8 = x ⋅ ( lo g 7 − lo g 2 )
( lo g 3 4 3 − lo g 2 2 8 ) / ( lo g 7 − lo g 2 ) = x
In conclusion: there is only one solution for x