How to Solve the Equation log(4x) = 1 + log(2, 2x)?

Wayne123 · 2009-12-06T22:02:32+00:00

Solve the equation log4x=1+log22x, x>0

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Start date Dec 6, 2009
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In summary, a logarithm is the inverse function of exponentiation and is used to represent the power to which a base number must be raised to obtain a given number. To solve logarithmic equations, the logarithm must be isolated and simplifed using properties such as the product, quotient, and power rules. The common properties of logarithms include the product, quotient, and power rules and can be used to simplify equations. The two most common types of logarithms are the natural logarithm (ln) and the common logarithm (log), but there are also other types with different bases. To check the solution to a logarithmic equation, you can plug it back into the original equation or use a graphing calculator to see if the

Dec 6, 2009

Wayne123

Solve the equation log₄x=1+log₂2x, x>0

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Dec 6, 2009

Mark44

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The form you started with had three sections, including relevant equations and your efforts at a solution. What are some relevant equations, and what have you tried to solve this equation?

BTW, this should have gone into the Precalculus section, not the Calculus & Beyond section.

FAQ: How to Solve the Equation log(4x) = 1 + log(2, 2x)?

What is a logarithm?

A logarithm is the inverse function of exponentiation. It represents the power to which a base number must be raised to obtain a given number. For example, the logarithm base 2 of 8 is 3, because 2 to the power of 3 equals 8.

How do I solve a logarithmic equation?

To solve a logarithmic equation, you must isolate the logarithm on one side of the equation and then use the properties of logarithms (such as the product, quotient, and power rules) to simplify it. Once the logarithm is simplified, you can exponentiate both sides to solve for the variable.

What are the common properties of logarithms?

The common properties of logarithms include the product rule (log_b(xy) = log_b(x) + log_b(y)), the quotient rule (log_b(x/y) = log_b(x) - log_b(y)), and the power rule (log_b(xⁿ) = n * log_b(x)). These properties can be used to simplify logarithmic equations.

What are the different types of logarithms?

The two most common types of logarithms are the natural logarithm (ln), which has a base of e (approximately 2.718), and the common logarithm (log), which has a base of 10. Other types of logarithms include base 2 logarithms (log₂), base 3 logarithms (log₃), and so on.

How can I check if my solution to a logarithmic equation is correct?

You can check your solution by plugging it back into the original equation and seeing if it satisfies the equation. You can also use a graphing calculator to graph both sides of the equation and see if they intersect at the solution.