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## UMULAS 2 years ago What is the solution to the equation log 2 x – log 2 3 = 2 ?

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1. psi9epsilon

is it log 2x or is it log x to the base 2, and also log 23 or log 3 to base 2

2. psi9epsilon

please retype the question

3. nphuongsun93

$\huge \log_2 x - \log_2 3 = 2$this i guess

4. UMULAS

yes the one the np did

5. UMULAS

I mean as usual logs i didd x - = 2 3 But the answer is not 6.

6. nphuongsun93

$\huge \log_2 x = 2+ \log_2 3$$\huge 2^{\log_2 x} = 2^{2 + \log_2 3}$$\huge x = 2^2 \times 2 ^{\log_2 3}$$x = 4 \times 3$

7. UMULAS

\_/ what how did you get he log and the 2 together?

8. nphuongsun93

o.O which one, how to type it or how to do it?

9. UMULAS

how to do it.

10. nphuongsun93

$\huge \log_2 x = 2 + \log_2 3$then 2^(everything)$\huge 2^{\log_2 x} = 2^{2+\log_2 3}$$\huge 2^{\log_2 x} = x$and the other side using a^(m+n) = a^m * a^n $\huge 2^{2+\log_2 3} = 2^2 \times 2 ^{\log_2 3} = 4 \times 3$

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