Math topics

Solving Logarithmic Equations

Solving Logarithmic Equations

Do you want to know how to solve Logarithmic Equations? you can do it in two easy steps. Step by step guide to solve Logarithmic Equations Convert the logarithmic equation to an exponential equation when it’s possible. (If no base is indicated, the base of the logarithm is 10) Condense logarithms if you have more than one log on one side of the equation. Plug in the answers back into the original equation and check to see the solution works. Example 1: Find the value of the variables in each equation. \(\log_{4}{(20-x^2)}=2\) Answer: Use log rule:...
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Natural Logarithms

Natural Logarithms

Do you want to know how to solve Natural Logarithms? you can do it in two easy steps. Step by step guide to solve Natural Logarithms A natural logarithm is a logarithm that has a special base of the mathematical constant e, which is an irrational number approximately equal to 2.71. The natural logarithm of x is generally written as ln x, or \(\log_{e}{x}\). Example 1: Solve the equation for \(x\): \(e^x=3\) Answer: If \(f(x)=g(x),then: ln(f(x))=ln(g(x))→ln(e^x)=ln(3) \) Use log rule: \(\log_{a}{x^b}=b \log_{a}{x}\), then: \(ln(e^x)=x ln(e)→xln(e)=ln(3)...
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Properties of Logarithms

Properties of Logarithms

Do you want to know how to Properties of Logarithms? you can do it in two easy steps. Step by step guide to Properties of Logarithms Learn some logarithms properties: \(a^{\log_{a}{b}}=b\)\(\log_{a}{1}=0\)\(\log_{a}{a}=1\)\(\log_{a}{x.y}=\log_{a}{x}+\log_{a}{y}\)\(\log_{a}{\frac{x}{y}}=\log_{a}{x}-\log_{a}{y}\)\(\log_{a}{\frac{1}{x}}=-\log_{a}{x}\)\(\log_{a}{x^p}=p\log_{a}{x}\)\(\log_{x^k}{x}=\frac{1}{x}\log_{a}{x}, for k\neq0\)\(\log_{a}{x}=\log_{a^c}{x^c}\)\(\log_{a}{x}=\frac{1}{\log_{x}{a}}\) Example 1: Expand this logarithm. \(log ⁡(8×5)=\) Answer: Use...
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Evaluating Logarithms

Evaluating Logarithms

Do you want to know how to solve Evaluating Logarithms? you can do it in two easy steps. Step by step guide to Evaluating Logarithms Logarithm is another way of writing exponent. \(\log_{b}{y}=x\) is equivalent to \(y=b^x \) Learn some logarithms rules: \(\log_{b}{(x)}=\frac{\log_{d}{(x)}}{\log_{d}{(b)}}\)\( \log_{a}{x^b}=b\log_{a}{x}\) \(\log_{a}{1}=0\) \(\log_{a}{a}=1\) Example 1: Evaluate: \(\log_{2}{16}\) Answer: Rewrite 16 in power base form: \(16=2^4\) , then: \(\log_{2}{16}=\log_{2}{(4^2)}\) Use log rule: \( \log_{a}{x^b}=b\log_{a}{x}\), then:...
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Math Formulas

Math Formulas

$$ x = x^2 $$ you can write formula inline : \(x = x^2 \) this...
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