Solve for x in terms of b (1)/(3) logb(x^3)+(1)/(2) logb(x^2-2 x+1)=2

Name: Problem 99, Chapter 3: Precalculus
Uploaded: 2020-07-01T19:59:44-08:00
Duration: 6 min 4 s
Channel: Himanshu Kushwaha
Description: Solve for x in terms of b (1)/(3) logb(x^3)+(1)/(2) logb(x^2-2 x+1)=2

step 1 So solving this logarithmic equation as 1 upon 3, log at base b is x cubed plus 1 upon 2, log ba

Solve for x in terms of b (1)/(3) logb(x^3)+(1)/(2)...

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Key Concepts

Properties of Logarithms

Understanding the properties of logarithms, such as the power rule, product rule, and quotient rule, is essential for simplifying and combining logarithmic expressions. These properties allow you to move coefficients as exponents, combine multiple logarithmic terms into a single term, or separate them, facilitating the process of solving equations.

Inverse Relationship Between Exponentiation and Logarithms

Recognizing that exponentiation is the inverse of taking logarithms enables you to convert a logarithmic equation into an equivalent exponential form. This transformation is a key step in isolating the variable and solving the equation, as it eliminates the logarithm and provides a direct algebraic expression to work with.

Algebraic Manipulation and Factoring

After applying logarithmic properties, the resulting expressions often require further algebraic manipulation, such as factoring or expanding, to isolate the variable of interest. Proficiency in these techniques is critical for simplifying equations and ultimately solving for the unknown variable.

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