Given that , what is the value of ?
Can someone show me how to solve this please? Cheers x
Or you can use the facts that $\displaystyle \log_b5^{1/2} = \tfrac12\log_b5$ and $\displaystyle \log_b5^4 = 4\log_b5$. Then the equation simplifies to $\displaystyle \log_b5=4$, which you should be able to solve on a calculator.
I deleted my original post in this thread after seeing the other replies thinking I had made an awfull mistake, but looking at these replies I see that they are addressing the problem:
$\displaystyle -2 \log_b(5^{1/2})+5\log_b(5^4)=76$
which seems natural enough because it can be solved in close form.
However that is not my reading of the question, which was to solve:
$\displaystyle -2^{ \log_b(5^{1/2})}+5^{\log_b(5^4)}=76$
which is somewhat different! and I stand by my earlier now deleted post and suggest graphical and/or numerical solution for this.
There is a real solution is close to $\displaystyle b=10.84$.
CB