How do you solve the exponential equation $9^x=3^(x+27)$ ?

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Answer 1 · 2017-03-05T17:04:17

We have that

$9^x=3^(x+27)$

$3^(2x)=3^x*3^27$

$3^(2x)/3^x=(3^x*3^27)/3^x$

$3^x=3^27$

$x=27$

Answer 2 · 2017-03-05T18:00:37

$color(red)(x=27$

$9^x=3^(x+27)$

$3^(2x)=3^(x+27)$

multiplyL.H.S. and R.H.S. by $color(red)(1/3$

$color(red)1/cancelcolor(red)3 xx cancelcolor(red)3^(2x)/color(red)1=(cancelcolor(red)3^(x+27))/color(red)1 xx color(red)1/cancelcolor(red)3$

$2x=x+27$

$2x-x=27$

$color(red)(x=27$

How do you solve the exponential equation 9^x=3^(x+27)9^x=3^(x+27)?