Question

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2. \ln (2 x+5)=\ln 3+\ln (x-1)

Answer 1

`\ln(2x+5) = \ln(3) + \ln(x-1)`

Recall the log property :

`log_(a)(b \cdot c)= log_(a)(b) + log_(a)(c)`

Hence we could simplify the equation into

`\ln(2x+5) = \ln(3(x-1))`

`\ln(2x+5) = \ln(3x-3))`

Recall the log property :

`a^{log_(a)(b)} = b`

Therefore if we raise
`e` by natural log power

`e^(\ln(2x+5)) &=& e^(\ln(3x-3)) \\ 2x+5 &=& 3x-3 \\ 3x - 2x &=& 5 + 3 \\ x &=& 8`

Hence the solution is x=8