Halils Methods questions

[Halil]

Just like i do for specialist ill post up questions here that I require help with.

Start with this one:

((log(x,10))/(log(2,10)))=4 find x

answer is 16, its a few clicks answer with the calculator, but what is the manual solution?

[simonhu81292]

isn't the answer 2^(1/4)?

[xZero]

This requires the knowledge of base changing in logs (no longer required since CAS has the ability to change base )

[Halil]

no, switch the positions of the x and 10, and the 2 and 10.
lol

[m@tty]

I would go:



(reciprocate both sides) - see note below




It's a bit shorter than your method, xZero


Note:

When "flipping" a log, the base  and number inside the log are switched:

ie.

So when the log fraction is flipped we switch the base and "number" in each.

[simonhu81292]

you would approach it the same was as shown
log10^x = 4 x log10^2
same base..log 10 cancels out
x = 2^4
x= 16

[m@tty]

no, switch the positions of the x and 10, and the 2 and 10.
lol

So the question is meant to be

 

If so, then use the change of base rule

[Halil]

thanks for that  M@tty, and others who tried

[Halil]

Next questions are related with the Log chapter.

Couldn't figure our how to do these two:

solve for x, where b is subset (the e looking icon thats facing right) of R -

and solve for x, where a is subset of R -

Ill try hard to find the solution, but after doing a 5.5 hour study on methods, my brain just stopped.

Any help will be appreciated greatly

(btw, it is 4 to the power of 2x-b, and 2 to the power of x-1 and 3 to the power of x+a, i dont know why the thing made it look like that)

Mod Edit: Fixed LaTeX

PS. Try curly brackets {...} when the power has multiple characters (or log base etc. )

[m@tty]

1.

[kamil9876]

means that





2)







Now solve for

edit: you could've taken some other base, 10 was arbitrary, it's just a habit developed from using shit calculators.

[Halil]

The answer for that first one is apparantly  


:S

[m@tty]