How do you solve $11.3^(2x – 1) = 15.7$ ?

Question

1132 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-28T13:57:26

I found: $x=1.0678$

Here I would use the natural log on both sides and one property of logs (about the exponent of the argument):

I write:

$color(red)(ln)11.3^(2x-1)=color(red)(ln)15.7$

then:

$(2x-1)ln(11.3)=ln(15.7)$

rearrange:
$2x-1=(ln(15.7))/(ln(11.3))$
$2x=(ln(15.7))/(ln(11.3))+1$
$x=[(ln(15.7))/(ln(11.3))+1]/2=1.0678$

How do you solve 11.3^(2x – 1) = 15.711.3^(2x – 1) = 15.7?