# Math Help - logarithmic problem :|

1. ## logarithmic problem :|

Given that , what is the value of ?

Can anyone help me with this? Cheers x

2. Originally Posted by Haris
Given that , what is the value of ?

Can anyone help me with this? Cheers x
I assume that you mean:

$-2\cdot \log_b \left(5^{\frac12}\right)+5 \cdot \log_b \left(5^{4}\right) = 76$ ............. If so:

$-2\cdot \frac12 \cdot \log_b (5)+5 \cdot 4 \cdot \log_b (5) = 76$

$- \log_b (5)+20 \cdot \log_b (5) = 76$

$\log_b(5)=\dfrac{76}{19}=4$

$5 = b^4~\implies~\boxed{b=\sqrt[4]{5}}$