AS Pure Chapter 14: Exponentials and Logarithms

16 flashcards · Mathematics · by TheoTyson

1. If f(x)=exf(x) = e^xf(x)=ex , then what is f′(x)f'(x)f′(x) ?

   f′(x)=exf'(x) = e^xf′(x)=ex

2. If f(x)=ekxf(x) = e^{kx}f(x)=ekx , then what is f′(x)f'(x)f′(x) ?

   f′(x)=kekxf'(x) = ke^{kx}f′(x)=kekx

3. What is log⁡an=x\log_a{n} = xloga​n=x equivalent to?

   ax=na^x = nax=n

4. What is log⁡ax+log⁡ay\log_a{x} + \log_a{y}loga​x+loga​y equal to?

   log⁡ax+log⁡ay=log⁡axy\log_a{x} + \log_a{y} = \log_a{xy}loga​x+loga​y=loga​xy

5. What is log⁡ax−log⁡ay\log_a{x} - \log_a{y}loga​x−loga​y equal to?

   log⁡ax−log⁡ay=log⁡a(xy)\log_a{x} - \log_a{y} = \log_a{(\frac{x}{y})}loga​x−loga​y=loga​(yx​)

6. What is log⁡a(xk)\log_a{(x^k)}loga​(xk) equal to?

   log⁡a(xk)=klog⁡ax\log_a{(x^k)} = k \log_a{x}loga​(xk)=kloga​x

7. What is log⁡a(1x)\log_a{(\frac{1}{x})}loga​(x1​) equal to?

   log⁡a(1x)=−log⁡ax\log_a{(\frac{1}{x})} = - \log_a{x}loga​(x1​)=−loga​x

8. What is log⁡aa\log_a{a}loga​a equal to?

   log⁡aa=1\log_a{a} = 1loga​a=1

9. What is log⁡a1\log_a{1}loga​1 equal to?

   log⁡a1=0\log_a{1} = 0loga​1=0

10. What is the asymptote of the graph y=exy = e^xy=ex ?

    xxx -axis.

11. What is the asymptote of the graph y=ln⁡xy = \ln{x}y=lnx ?

    yyy -axis.

12. What are the graphs of y=exy = e^xy=ex and y=ln⁡(x)y = \ln(x)y=ln(x) ?

13. If y=axny = ax^ny=axn is plotted as log⁡y\log{y}logy against log⁡x\log{x}logx , then what is the gradient?

    The gradient is nnn .

14. If y=axny = ax^ny=axn is plotted as logylog{y}logy against log⁡x\log{x}logx , then what is the yyy -intercept?

    The yyy -intercept is log⁡a\log{a}loga .

15. If y=abxy=ab^xy=abx is plotted as log⁡y\log{y}logy against xxx , then what is the gradient?

    The gradient is log⁡b\log{b}logb .

16. If y=abxy=ab^xy=abx is plotted as log⁡y\log{y}logy against xxx , then what is the yyy -intercept?

    The yyy -intercept is log⁡a\log{a}loga .