Given that , what is the value of ?
Can anyone help me with this? Cheers x
I assume that you mean:
$\displaystyle -2\cdot \log_b \left(5^{\frac12}\right)+5 \cdot \log_b \left(5^{4}\right) = 76$ ............. If so:
$\displaystyle -2\cdot \frac12 \cdot \log_b (5)+5 \cdot 4 \cdot \log_b (5) = 76$
$\displaystyle - \log_b (5)+20 \cdot \log_b (5) = 76$
$\displaystyle \log_b(5)=\dfrac{76}{19}=4$
$\displaystyle 5 = b^4~\implies~\boxed{b=\sqrt[4]{5}}$