Question

Help please I’m not sure what the answer for this one is no need to explain

Answer 1

Answer:

b.  e^9.45 = x

see last example and this explains whole numbers and decimals.

Step-by-step explanation:

Another example we can Solve  100=20e^2t .

Solution

100 = 20e^2t

5 = 20e ^2t

in 5 = 2t

Therefore  t = in5/ 2

Step 1 was ; Divide by the coefficient of the power

Step 2 was ; Take ln of both sides. Use the fact that ln(x) and ex are inverse functions

Step 3 was; Divide by the coefficient of t

Another example;

Solve  e^2x−e^x = 56 .

Solution

Analysis

When we plan to use factoring to solve a problem, we always get zero on one side of the equation, because zero has the unique property that when a product is zero, one or both of the factors must be zero. We reject the equation  e^x=−7  because a positive number never equals a negative number. The solution  ln(−7)  is not a real number, and in the real number system this solution is rejected as an extraneous solution.

Another example is;

Solve  e^2x=e^x+2 .

Answer

Q&A: Does every logarithmic equation have a solution?

No. Keep in mind that we can only apply the logarithm to a positive number. Always check for extraneous solutions.

Last example determines decimals ;

Solve  lnx =3 .

Solution

lnx^x=3=e^3

Use the definition of the natural logarithm

 

Graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to  20 . In other words  e^3≈20 . A calculator gives a better approximation:  e^3≈20.0855 .

The graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to  20 . In other words  e^3≈20 . A calculator gives a better approximation:  e^3≈20.0855 .

It shows values of graphs of  y=lnx  and  y=3  cross at the point  (e^3,3) , which is approximately  (20.0855,3) .

See graph below.