Find the limit: $\lim_{x\to 0} \frac{8^x-7^x}{6^x-5^x}$ Find the limit:
$$\lim_{x\to 0} \frac{8^x-7^x}{6^x-5^x}$$
I really have no idea what to do here, since I obviously can't plug in $x=0$ nor divide by highest power...Any help is appreciated!

By using hint of @dxix we get 
$$\lim _{ x\to 0 } \frac { 8^{ x }-7^{ x } }{ 6^{ x }-5^{ x } } =\lim _{ x\to 0 } \frac { { 7 }^{ x }\left[ { \left( \frac { 8 }{ 7 }  \right)  }^{ x }-1 \right]  }{ { 5 }^{ x }\left[ { \left( \frac { 6 }{ 5 }  \right)  }^{ x }-1 \right]  } =\lim _{ x\to 0 } \frac { { 7 }^{ x }\frac { \left[ { \left( \frac { 8 }{ 7 }  \right)  }^{ x }-1 \right]  }{ x }  }{ { 5 }^{ x }\frac { \left[ { \left( \frac { 6 }{ 5 }  \right)  }^{ x }-1 \right]  }{ x }  } =\\ =\frac { \ln { \left( 8/7 \right)  }  }{ \ln { \left( 6/5 \right)  }  } $$
