How do you solve $5^(x - 1) = 3^x$ ?

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Answer 1 · 2016-02-11T04:09:41

You must first convert to logarithmic form.

$log5^(x - 1) = log3^x$

$(x - 1)log5 = xlog3$

Distribute the parentheses:

$xlog5 - log5 = xlog3$

Put all x terms to the left side of the equation:

$xlog5 - xlog3 = log5$

Factor out the x:

$x(log5 - log3) = log5$

Use the quotient rule:

$x(log(5/3)) = log5$

$x = log5/(log(5/3)$

$x = log_(5/3)5$

Practice exercises:

a) $2^(x - 2) = 3^(2x + 4)$

b) $3^(3x) = 4 xx 5^(x - 6)$

Good luck!

How do you solve 5^(x - 1) = 3^x 5^(x - 1) = 3^x?