Solve the logarithmic equation. Express irrational solutions in exact form and a

Charles Cisneros

Charles Cisneros

Answered question

2021-11-06

Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.
log(x1)=(13)log2

Answer & Explanation

juniorekze

juniorekze

Beginner2021-11-07Added 18 answers

Step 1
The equation is a statement that consists of equal symbol between two algebraic expressions. The solution for the variable of the equation must satisfy the equation when we resubstitute the solution in the equation. The given equation involves logarithm terms.
A logarithm is the power to which a number must be raised in order to get some other number. Example is if loga(x)=b  then  x=ab. Here a is the base of the logarithm. The common logarithms are logarithms with base 10 and these are represented with log(x).
Step 2
The given equation contains common logarithm on both sides. To solve the given equation solve using logarithm properties as follows;
log(x1)=(13)log2  .........Given equation.
log(x1)=log213  ...........Use: If  alog(x)=log(xa)
x1=213  ...........As base of both logarithms are same, equate the terms.
x1=3{2}
x=1+3{2}  ...........Add both sides with 1.
x=1+3{2}  ............Solution in exact form.
Hence, the solution of the given equation asked in the question in exact form is x=1+3{2}

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