Solve the logarithmic equation. Express irrational solutions in

avalg10o

avalg10o

Answered question

2022-03-20

Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.
log5(2x+3)=log53

Answer & Explanation

Endstufe5qa2

Endstufe5qa2

Beginner2022-03-21Added 7 answers

Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to perform arithmetic operation on them. Multiplication and division can be written in form of addition and subtraction while operating logarithms.
There are various rules involved in performing logarithmic operations, some required for question are as follows
Product rule logamlogan=logamn
Exponent rule logam=xm=ax
If the base of logarithm on both sides of equation is constant, then the argument of both sides are also equal. Consider the case of given equation log5(2x+3)=log53. Here the base of both sides of equation is equal therefore, the argument will also be equal. Equate the argument to get value of x
log5(2x+3)=log53
2x+3=3
2x=33
2x=0
x=0
Therefore, solution of equation log5(2x+3)=log53 for x is 0.

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