Question

Question #27c70

Answer 1

`x≈4.090" to 3 dec. places"`

Explanation:

Isolate the exponential by dividing both sides by 40

`rArr(1.5)^x=210/40=21/4`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(logx^n=nlogx)color(white)(2/2)|)))`

Take the ln ( natural log) of both sides.

`rArrln(1.5)^x=ln(21/4)`

`rArrxln(1.5)=ln(21/4)`

`rArrx=(ln(21/4))/(ln1.5)≈4.090" to 3 dec.places"`