Question

Consider the equation 0.75⋅10^w/3=30

Answer 1

Answer:

The value of w is:

$w=3\cdot log_{10}(40)$

Step-by-step explanation:

We have to calculate w from the equation

$0.75\cdot 10^{w/3}=30$

The solution has to be expressed as a logarithm in base 10.

We can solve it like:

$0.75\cdot10^{w/3}=30\\\\10^{w/3}=30/0.75=40\\\\(w/3)log_{10}(10)=log_{10}(40)\\\\w/3=log_{10}(40)\\\\w=3\cdot log_{10}(40)$

The value of w is:

$w=3\cdot log_{10}(40)$