# Tag Archives: Equation Logarithmic Equations Reducible to Quadratic of Math Online Tutoring is based on the basic properties of logarithms such as;$$\displaystyle\log_{a}{b} = \frac{1}{\log_{b}{a}} \\\log_{a}{b} = \frac{\log_{c}{b}}{\log_{c}{a}} \\$$ Question 1 Solve $2 \log_{2}{x} – 9 \log_{x}{2} = 3$. \begin{aligned} \displaystyle2 \log_{2}{x} – \frac{9}{\log_{2}{x}} &= 3 \\2 (\log_{2}{x})^2 – 9 &= 3 \log_{2}{x} \\2 (\log_{2}{x})^2 – […] # Exponential Equations Reducible to Quadratics Exponential Equations Reducible to Quadratic for Math Help is based on various index rules, such as; a^{x+y} = a^x \times a^y \\(a^x)^y = a^{xy}  Question 1 Solve \( 9^x – 10 \times 3^x + 9 = 0. \begin{aligned} \displaystyle \require{color}(3^x)^2 – 10 \times 3^x + 9 &= 0 &\color{red} 9^x = (3^2)^x […] # Equations Reducible to Quadratic by Substitution Equations Reducible to Quadratic by Substitution to Learn Math is made the equations easy to solve by substitution to simplify the equations. Question 1 Solve \( (x+2)^2 – 3(x+2) – 4 = 0. \begin{aligned} \displaystyle \require{color}\text{Let } A &= x+2 \\A^2 – 3A -4 &= 0 &\color{red} \text{replace } x+2 \text{ by } […] # Fraction Equations Reducible to Quadratic iitutor provides full explains of Fraction Equations Reducible to Quadratic for Free Math Help. \( \begin{aligned} \displaystyle \require{color} x+\frac{a}{x} &= b \\ x^2 + a &= bx \\ x^2 – bx + a &= 0 \\ \end{aligned} Once, the equation forms a quadratic form by multiply the denominator to both sides, then the equation […] # 4 Important Types of Absolute Value Equations

There are 4 main types of absolute value equations regarding whether there are; absolute value and a static value absolute value and an expression involving unknown pronumerals two absolute values in both sides two absolute values and a value Type 1: One Absolute Value and a Constant Solve $| x-2 | = 5$. […] Solving radical equations are required to isolate the radicals or surds to one side of the equations. Then square both sides. Here we have two important checkpoints. Checkpoint 1 for Solving radical equations Make sure the whole both sides are to be squared but not squaring individual terms. This is what I say, $$(1+2)^2 = […] # 12 Patterns of Logarithmic Equations Solving logarithmic equations is done many ways using properties of logarithmic functions, such as multiply of logs, change the base and reciprocals of logarithms.$$ \begin{aligned} \displaystyle \large a^x = y \ &\large \Leftrightarrow x = \log_{a}{y} \\ \large \log{a} + \log{b} &= \large \log{(a \times b)} \\ \large \log{a} – \log{b} &= \large \log{(a […] For solving Quadratic Equations in Square Roots, it is required to square both sides entirely, but not individually. For instance, $$(1 + 2)^2 = 3^2 \\ 1^2 + 2^2 \ne 3^2$$ It is important to check the solutions to see they work for the original equation, if the original equation is squared. Worked […]