Problems from An introduction to exponential equation

Development:

a) $9^x=2\Rightarrow x=lo{g}_{9}2$

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

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

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

Re-writing and operating: $3+3^y-1=5\Rightarrow 3^y=3\Rightarrow y=lo{g}_{3}3=1$

Solution:

a) $x=lo{g}_{9}2$

b) $y=1$

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