37+(20log6000)+(20log30)

Good effort but I don't think that is completely correct.

We have to use a few identities here

$$nloga=log(a^n)$$

  $$loga+logb=log(ab)$$

$$a^nb^n=(ab)^n$$

$$37+(20log6000)+(20log30)\\ =37+log(6000^{20})+log(30^{20})\\ =37+log(6000^{20}30^{20})\\ =37+log(6000*30)^{20}\\ =37+log(180000^{20})\\ =37+20log(180000)\\$$

I think that is correct!

When logs are used in addition, they can also be written as multiplication. You can combine these logs in the form  of multiplication.

You should rewrite the coeffecient of 20 as an exponent in both logs.

37 + (log6000^20) + (log30^20)

Rewrite in the form of multiplication. Keep the log and mulitiply the numbers of the log.

37 + log(6,000*30)^40      The exponents were added, because of multiplication.

37 + log180,0000^40

Might be simpler to factor the 20 first:

37 + 20*(log6000 + log30)

37 + 20*log(6000*30)

37 + 20*log180000

$${\mathtt{37}}{\mathtt{\,\small\textbf+\,}}{\mathtt{20}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{180\,000}}\right) = {\mathtt{142.105\: \!450\: \!102\: \!066\: \!13}}$$