if log3base 30=a & log5base 30=b,find the value of log8base 30
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given:㏒3 base 30=a.....(1) and ㏒ 5 base 30=b...(2)
let x=㏒₃₀8=㏒₃₀2³⇒x=3㏒₃₀2=c.....(3)
adding eq(1),eq(2) and eq(3)/3 we have
㏒₃₀3+㏒₃₀5+㏒₃₀2=a+b+c/3
㏒₃₀3ˣ5ˣ2=a+b+c/3
㏒₃₀30=a+b+c/3
a+b+c/3=1
c/3=1-a-b
c=3(1-a-b)
but from eq(3)
c=㏒₃₀8
so ㏒₃₀8=3(1-a-b)
let x=㏒₃₀8=㏒₃₀2³⇒x=3㏒₃₀2=c.....(3)
adding eq(1),eq(2) and eq(3)/3 we have
㏒₃₀3+㏒₃₀5+㏒₃₀2=a+b+c/3
㏒₃₀3ˣ5ˣ2=a+b+c/3
㏒₃₀30=a+b+c/3
a+b+c/3=1
c/3=1-a-b
c=3(1-a-b)
but from eq(3)
c=㏒₃₀8
so ㏒₃₀8=3(1-a-b)
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