113k views
5 votes
Solve the following logarithmic equation and round to the nearest tenth:
2log₃x + log₃4 = 4

User Aea
by
8.9k points

1 Answer

2 votes

Final answer:

To solve the logarithmic equation 2log₃x + log₃4 = 4, we use properties of logarithms to combine the terms and then exponentiate to remove the logarithm. This leads to a quadratic equation 4x^2 = 81, which simplifies to x = 4.5 when rounded to the nearest tenth.

Step-by-step explanation:

To solve the following logarithmic equation and round to the nearest tenth, 2log₃x + log₃4 = 4, we use logarithm properties and algebra.

Firstly, apply the power rule of logarithms alog₃x = log₃(x^a) which simplifies our equation to:

log₃(x^2) + log₃4 = 4

Next, apply the product rule log₃x + log₃y = log₃(xy) which results in:

log₃(4x^2) = 4

We then need to remove the logarithm by exponentiating both sides with base 3:

3^log₃(4x^2) = 3^4

This simplifies further to:

4x^2 = 81

Now, divide both sides by 4:

x^2 = 20.25

x = ±√20.25

Since we are generally interested in positive solutions for x:

x ≈ 4.5 when rounded to the nearest tenth.

User HAxxor
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.