Question

Consider the equation 0.75⋅10^w/3=30

Solve the equation for w. Express the solution as a logarithm in base-10

Answer 1

The value of w is:

`w=3\cdot log_(10)(40)`

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)`