Question

2^x=3^x+1 what are the exact approximate solutions

Answer 1

D edge

Explanation:

Answer 2

The exact approximate solution is x=-3.

Explanation:

Given : Expression
`2^x=3^(x+1)`

To find : What are the exact approximate solutions?

Solution :

Step 1 - Write the expression

`2^x=3^(x+1)`

Step 2 - Taking log both side,

`\log(2^x)=\log(3^(x+1))`

Step 3 - Applying logarithmic property,
`\log a^x=x\log a`

`x\log(2)=(x+1)\log(3)`

Step 4 - Solve

`x(\log(2)-\log(3))=\log(3)`

`x=(\log(3))/((\log(2)-\log(3)))`

`x=(\log(3))/(\log((2)/(3)))`

`x=(0.477)/(-0.176)`

`x=-2.710\approx -3`

Therefore, The exact approximate solution is x=-3.