What is log5x-1=3, is it log(5x-1)=3 or log(5x)-1=3?

Question

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Answer 1

If this is exactly the way it's written...

 

log5x-1=3

 

...then it means log(5x)-1=3

 

To solve...

 

log (5x) - 1 = 3

 

Add 1 to both sides:

log (5x) = 4

 

Exponentiate both sides, with a base of 10 (since log without a base means log₁₀):

10^{log (5x)} = 10⁴

 

Use the definition of log:

5x = 10000

 

x = 10000 / 5 = 2000

 

 

Answer 2

I take it what you're asking is what is x equal to in this equation.  If so, the solution of the problem goes like:

 

log5x = 4  (add one to both sides)

5x = 10^4  (make both sides the exponent of 10)

5x = 10,000  (raise 10 to the 4th)

x = 2,000  (divide both said by 5)