Question

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

Answer 1

Answer:

The exact approximate solution is x=-3.              

Step-by-step 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

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

$x=\frac{\log(3)}{(\log(2)-\log(3))}$

$x=\frac{\log(3)}{\log(\frac{2}{3})}$

$x=\frac{0.477}{-0.176}$

$x=-2.710\approx -3$

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

Answer 2

Answer:

D edge

Step-by-step explanation: