Solve 9^x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b.
a.) −3.094
b.) −2.909
c.) 4.916
d.) 5.091

If you meant , then the answer is approximately 0.866.

If you meant , then the answer is approximately -2.909 which looks like what you meant based on the choices.

Step-by-step explanation:

First step is to get the exponential part by itself. The part that has the variable exponent which is the term.

To do this we need to subtract 4 on both sides:

Simplify:

The equivalent logarithmic form is:

I always say to myself the logarithm is the exponent that is how I know what to put opposite the side containing the log.

Anyways if you don't have options for computing in your calculator you need to use the change of base formula.

So

I don't see this as a choice so maybe you actually meant the following equation:

Let's see if this is the correct interpretation.

So the exponential part is already isolated.

So we just need to put in the equivalent logarithmic form:

Now we subtract 4 on both sides:

Again if you don't have the option for computing in your calculator, you will have to use the change of base formula:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.