Question

4^x+4^x+1=80

3^45:3^30+x=3^7x{ori}3^8

Answer 1

"4^x+4^x+1=80 "

4^x + 4^(x+1) = 80      (!!!)

$\it 4^x+4^{x+1} =80 \Leftrightarrow 4^x+4\cdot4^x =80 \Leftrightarrow 4^x(1+4) = 80 \Leftrightarrow$

$\it \Leftrightarrow 4^x\cdot5 = 80|_{:5} \Leftrightarrow 4^x = 16 \Leftrightarrow 4^x=4^2 \Leftrightarrow x = 2.$
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"3^45:3^30+x=3^7x{ori}3^8"


3^45 : 3^30 + x = 3^7·3^8⇔3^(45-30) + x = 3^(7+8) ⇔ 3^15 + x = 3^15 ⇔ x = 0