What is the step by step way to solve this exponential equation?2^ (x+1) = 3^x

Question

Robert Maddox

Mathematics

6 October, 13:04

What is the step by step way to solve this exponential equation?2^ (x+1) = 3^x

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Answers (1)

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Lena Wagner · Answer 1

2⁽ˣ⁺¹⁾ = 3ˣ

ln[2⁽ˣ⁺¹⁾] = ln (3ˣ)

(x+1). ln (2) = x. ln (3)

Expand:

x. ln (2) + ln (2) = x. ln (3)

x. ln (2) - x. ln (3) = - ln (2)

x[ln (2) - ln (3) ] = - ln (2)

x = [ - ln (2) ] / [ln2) - ln (3)

And x = 1.7095