The diagram shows two curves ${{C}_{1}}$ and ${{C}_{2}}$ which represent $y=\ln \left( x+2 \right)$ and $y=\lg \left( x+2 \right)$ respectively, for $x>a$. State the value of $a$. Explain briefly if ${{C}_{1}}$ represents the graph of $y=\ln \left( x+2 \right)$ . Find the solution in which $\lg \left( x+2 \right)=\ln \left( x+2 \right)$.

Exponential and Logarithmic Functions - Sketching Logarithmic Functions and Solving Equations Graphically

IP 3

The diagram shows two curves ${{C}_{1}}$ and ${{C}_{2}}$ which represent $y=\ln \left( x+2 \right)$ and $y=\lg \left( x+2 \right)$ respectively, for $x>a$.

State the value of $a$.
Explain briefly if ${{C}_{1}}$ represents the graph of $y=\ln \left( x+2 \right)$ .
Find the solution in which $\lg \left( x+2 \right)=\ln \left( x+2 \right)$.

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Answer:(i) $a=-2$; (ii) $C_1$ represents $y=\ln(x+2)$; (iii) $x=-1$

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