log question (1 Viewer)

[Green Yoda]

Question 3D

 

[InteGrand]

Question 3D
View attachment 32163

 

[InteGrand]

Wait, they wanted you to do it like this:

 

[InteGrand]

(I.e. express both sides as powers of 2 using index laws and then equate indices.)

 

[Green Yoda]

thank you

 

[Green Yoda]

btw if this question was in an exponential base 10 form and there was a surd 16√2 you would just directly divide log 16√2 / log 8 instead of seperating the 16 and √2 into 2 logs?

 

[InteGrand]

btw if this question was in an exponential base 10 form and there was a surd 16√2 you would just directly divide log 16√2 / log 8 instead of seperating the 16 and √2 into 2 logs?

The surds they give you would generally be ones that are nice powers of the base. Like 16√2 is a nice power of 2, but not of 10, so they wouldn't give you something like 16√2 for powers of 10 and expect a nice answer.

The general way to solve an equation of the form is take log to the base a of both sides. Then use change of base formula to get it into base 10 or e so you can use your calculator to get a numerical approximation.