log 3base 7(3x^4) help with logorithmic differentiation

Question

Can someone please help me with this and take me through step by step i have a test on this tommorow 

Answer 1

We can use the change of base formula to convert to natural logarithms:

 

log₇(3x⁴) = ln(3x⁴) / ln7

 

              = [ln3 + ln(x⁴)] / (ln7)

 

              = [1 / ln7][ln3 + 4lnx]

 

So, the derivative is [1/ln7](0 + 4/x) = 4 / (xln7)