Problems from An introduction to exponential equation

Solve the following expressions:

a) $$9^x=2$$

b) $$3+(5-2)^y-1=\dfrac{25}{5}$$

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a) $$9^x=2 \Rightarrow x=log_9 2$$

b) $$3+(5-2)^y-1=\dfrac{25}{5}$$

Because of the hierarchy of the operations we firstly do what is in brackets: $$(5-2)=3$$

and then the quotients: $$\dfrac{25}{5}=5$$

Re-writing and operating: $$3+3^y-1=5 \Rightarrow 3^y=3 \Rightarrow y=log_3 3=1$$


a) $$x=log_9 2$$

b) $$y=1$$

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