Solve the following equation for the unknown quantity x. \mathrm{9^x=40} *Round to the nearest hundredth as needed*

Question

Solve the following equation for the unknown quantity x.


`\mathrm{9^x=40}`

*Round to the nearest hundredth as needed*

Answer 1

`x = 1.68`

Explanation:

We have the equation
9ˣ = 40 and we have to solve for x

Take logs on both sides

`\ln(9^x) = \ln(40)\\\\\ln(9^x) = x ln(9) \\\\\therefore x \ln(9) = \ln(40)\\\\x = (\ln(40))/(\ln(9))\\\\\text{Using a calculator, this works out to: }\\\\x=1.67888139\dots \\\\\text{Rounded to the nearest hundredth, }\\x = 1.68\\\\`