Question

10. Solve the following exponential equation. Round your answer to three decimal places.9(6^3x)=24 x =

Answer 1

Let's find x.

`\text{ 9(6}^(3x))\text{ }=\text{ 24}`

We get,

`\text{ 9(6}^(3x))\text{ }=\text{ 24}`
`(9\cdot\:6^(3x))/(9)=(24)/(9)`
`6^(3x)=(8)/(3)`

Applying the rules of exponent, we get:

`3x\ln \mleft(6\mright)=\ln \mleft((8)/(3)\mright)`
`x=(\ln((8)/(3)))/(3\ln(6))\text{ = }0.18247\ldots`
`x\text{ }\approx\text{ 0.182}`

Therefore, the answer is 0.182