# How to solve a log equation

\log _2(x+1)=\log _3(27) \ln (x+2)-\ln (x+1)=1 \ln (x)+\ln (x-1)=\ln (3x+12) 4+\log _3(7x)=10 \ln (10)-\ln (7-x)=\ln (x) \log _2(x^2-6x)=3+\log _2(1-x)

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## Logarithmic equations: variable in the argument (video)

Type 1. In this type, the variable you need to solve for is inside the log, with one log on one side of the equation and a constant on the other. Turn the variable inside the log into an

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## Solving Log Equations with Exponentials

Since we want to transform the left side into a single logarithmic equation, we

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## Solving Logarithmic Equations

Solve the logarithmic equation: $$\log_{2}(x+4)-\log_{2}(3)=\log_{2}(x-2)-\log_{2}(5)$$ Solution: Here, we have a logarithm subtraction on each side of the equation. We can use the quotient

## Solving Logarithmic Equations – Explanation & Examples

log(3x−2)−log(2) = log(x+4) log(3x−2 2) = log(x+4) Apply the quotient rule of logarithms. 3x−2 2 = x+4 Apply the one-to-one property. 3x−2 = 2x+8 Multiply both sides of the equation by 2. x = 10 Subtract 2x and add 2.