Solve lg(x-3)=4

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation to be solved is lg(x - 3) = 4

If the base of the log is 10:

lg(x - 3) = 4

=> x - 3 = 10^4

=> x = 10000 + 3

=> x = 10003

Else if the base is considered as b.

lg(x - 3) = 4

=> x - 3 = b^4

=> x = b^4 + 3

The solution of the equation is x = b^4 + 3, where the base is b. If the base is 10, x = 10003

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll take antilogarithm:

lg(x - 3) = 4 <=> x - 3 = 10^4

We'll add 3 both sides:

x = 10^4 + 3

x = 10000 + 3

x = 10003

We'll verify if the number 10003 verifies the constraint of existence of logarithm:

x - 3 > 0

x > 3

We notice that 10003 > 3, therefore the solution of the equation is x = 10003.

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The equation log(x-3)=4 has to be solved.

As the base of the logarithm is not given it can be taken to be 10.

As logarithm are defined, if `log_b a = c` , `a = b^c`

As `log_10 (x - 3) = 4`

x - 3 = 10^4

x - 3 = 10000

x = 10003

The solution of the equation is 10003

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