Solving an Exponential Equation: 3e^x=10

[Illvoices]

How to solve for this equation? 3e^x=10

I tried and use the following to solve it but i got the wrong answer:
3e^x = 10 Given equation
e^x=10/3 Divide 3
1n e^x=1n3.3^e Take 1n of each side
x=3.3^​e

 

[JeffM]

How to solve for this equation? 3e^x=10

I tried and use the following to solve it but i got the wrong answer:
3e^x = 10 Given equation
e^x=10/3 Divide 3 This is fine.
1n e^x=1n3.3^e Take 1n of each side Taking the natural log is fine. But 10/3 is not 3.3, and the log of 3.3 is not 3.3^e.
x=3.3^​e In general, \(\displaystyle ln(p) \ne p.\)

Following up on denis:

\(\displaystyle 3e^x = 10 \implies ln(3e^x) = ln(10) \implies ln(3) + x * ln(e) = ln(10) \implies\)

\(\displaystyle ln(3) + x * 1 = ln(10) \implies x = ln(10) - ln(3) \approx 1.204\).

Or you can take denis' shortcut

\(\displaystyle 3e^x = 10 \implies e^x = \dfrac{10}{3} \implies x = \dfrac{ln \left ( \dfrac{10}{3} \right ) }{ln(e)} \implies\)

\(\displaystyle x = \dfrac{ln \left ( \dfrac{10}{3} \right ) }{1} = ln \left ( \dfrac{10}{3} \right ) \approx 1.204.\)

 

[stapel]

How to solve for this equation? 3e^x=10

I tried and use the following to solve it but i got the wrong answer:
3e^x = 10 Given equation
e^x=10/3 Divide 3
1n e^x=1n3.3^e Take 1n of each side
x=3.3^​e

Okay; guessing and trying to work backwards from the answers is clearly not working, because the answers provided at your various threads aren't seeming to make any sense to you. Instead, maybe think about taking a break and studying some lessons on this topic. For instance, here. But first learn what logarithms are: here

 

[Illvoices]

alright already ive understood the answer choice. thank you all for helping me out on this question, i will be adding parenthesis next time