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emma3001
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Solve the equation log2x + log4x= 5. To start, should I change this to an exponential... I am stuck because I have only done log questions that have the same base.
What do you mean by "log2x+ log4x= 5"? I would interpret that as log(2x)+ log(4x)= 5 so log(6x)= 5 which is easy. If you mean "log_2(x)+ log_4(x)= 5" then use Dick's hint.emma3001 said:Solve the equation log2x + log4x= 5. To start, should I change this to an exponential... I am stuck because I have only done log questions that have the same base.
Dick said:Convert them to the same base log_a(x)=log_b(x)/log_b(a).
A logarithm is the inverse of an exponential function. It is used to solve equations where the variable is in the exponent.
To solve for x in a logarithmic equation, you can use the properties of logarithms to rewrite the equation in a simpler form and then solve for x using algebraic techniques.
The three main properties of logarithms are the product rule, quotient rule, and power rule. These properties allow you to manipulate logarithmic equations and simplify them.
To solve a logarithmic equation, follow these steps:
1. Use the properties of logarithms to rewrite the equation in a simpler form.
2. Isolate the logarithmic expression on one side of the equation.
3. Convert the logarithmic expression into an exponential expression.
4. Solve for the variable using algebraic techniques.
5. Check your answer by plugging it back into the original equation.
Logarithms are used in a variety of fields, including finance, biology, and astronomy. They are useful for modeling exponential growth and decay, measuring the intensity of earthquakes and sound, and calculating pH levels in chemistry.