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So theres a question on one of my logarithm revision sheets that i have no idea how to solve, so i thought id come here to ask for your infinite mathematical wisdom.

Given that $\log_a(y)=\cfrac{3}{2}\ $ and $\log_4(a)=b+2$ Show that $y=2^p$ Where p is an expression in terms of b.

Thank you in advance ~

MrSuspicious
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Write the log expressions in exponential form,

$$a^{3/2}=y \;\;\; and \;\;\; 4^{b+2}=a.$$

Substituting $4^{b+2}$ in the first equation for $a$ and using exponent laws quickly yields, $$p=3b+6.$$

(Recall that $(a^{n})^{m}=a^{nm}$)

krazy-8
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  • Im plenty familiar with exponent laws, but for some reason i really didnt see it that way. Im new to logarithms so this is all rather confusing for the moment. But thank you so much for the help! :) – MrSuspicious Feb 01 '21 at 10:20
  • No worries. Exponentiation may sometimes be confusing with parentheses. Let me know if you require any additional clarification. Good luck with logarithms – krazy-8 Feb 01 '21 at 10:28