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12-10-2021
Mathematics

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*please help! lots of points and brainiest to right answer!2^x+1 = 5^3x
find the exact solution for x using logarithms and isolating x

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Аноним Аноним

05-05-2022

[tex]\\ \rm\Rrightarrow 2^{x+1}=5^{3x}[/tex]

[tex]\\ \rm\Rrightarrow ln2^{x+1}=ln5^{3x}[/tex]

[tex]\\ \rm\Rrightarrow (x+1)ln2=3xln5[/tex]

[tex]\\ \rm\Rrightarrow xln2+ln2=3xln5[/tex]

[tex]\\ \rm\Rrightarrow ln2=3xln5-xln2[/tex]

[tex]\\ \rm\Rrightarrow ln2=x(3ln5-ln2)[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{ln2}{3ln5-ln2}[/tex]

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