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# Logarithmic equations

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So the equation i've got from the question is

4 = 10log10(S1/40)

next I use the rules of logs to rearrange the equation

4 = log10((S1/40)10)

then take the log10 of both sides

0.602 = (S1/40)10

Assuming I have done everything right so far. Where do I take this equation next?

Jan 1, 2018

#1
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4 = 10log10(S1/40)

4 = log10((S1/40)10)

Now raise both sides to the power of 10

10^4=10^(log10((S1/40)10)

10000=(S1/40)^10

(10000)^(0.5)=((S1/40)^10)^0.5

100=(S1/40)^5

100*40^5 = S1^5

100*10^5*4^5=S1^5

10 000 000*4^5=S1^5

4*10^(1.4)=S1

S1=100.47  approx

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That was really messy, I will try and check it.

4 = 10log10(S1/40)

0.4=log10(S1/40)

10^0.4=S1/40

40*10^0.4=S1

S1 = 100.47  approx

The second method is much better !!

Jan 2, 2018

#1
+2

4 = 10log10(S1/40)

4 = log10((S1/40)10)

Now raise both sides to the power of 10

10^4=10^(log10((S1/40)10)

10000=(S1/40)^10

(10000)^(0.5)=((S1/40)^10)^0.5

100=(S1/40)^5

100*40^5 = S1^5

100*10^5*4^5=S1^5

10 000 000*4^5=S1^5

4*10^(1.4)=S1

S1=100.47  approx

---

That was really messy, I will try and check it.

4 = 10log10(S1/40)

0.4=log10(S1/40)

10^0.4=S1/40

40*10^0.4=S1

S1 = 100.47  approx

The second method is much better !!

Melody Jan 2, 2018