Match the equation with the correct solution.
log 4 x + log 4 9 = log 4 27

Question

Match the equation with the correct solution.
log 4 x + log 4 9 = log 4 27

anonymous · Answer

here are the answer choices
3
2
-2
5
12
4

turingtest · Answer

use the log property$$\large \log_a x+\log_a y=\log_a(xy)$$to combine the terms on the left, then raise 4 to the power of both sides to get rid of the logarithm$$\huge a^{\log_ax}=x$$

anonymous · Answer

how do i do that?

turingtest · Answer

well for instance$$\log5+\log2=\log(5\times2)=\log(10)$$do that trick with the terms on the left hand side of your equation

anonymous · Answer

can i plug that into my calc?

campbell_st · Answer

use log laws for addition 

$$loa_{a} b + \log_{a} c = \log_{a} bc$$

so you have on the left hand side

$$\log_{4} x + \log_{4} 9 = \log_{4} 9x $$

so solve 9x = 27

turingtest · Answer

using logs with bases other than 10 or e is not common to many calculators
best to go about it by hand

anonymous · Answer

huh?

turingtest · Answer

@campbell_st used exactly what I said above, and in my opinion gave a bit too much info
you should certainly be able to take it from where he left off.

anonymous · Answer

yes i got 3 but how did he get to that point?

anonymous · Answer

how did he get 9x=27?

campbell_st · Answer

because the logs are in the same form... 


$$\log_{4} 9x = \log_{4} 27$$

you can just equate the 9x and 27