1 Answer

Jason Grife · Answer 1 · 2023-12-22T23:49:24+0000

Hello there. To solve this question, we'll have to apply some logarithm properties to rewrite the number and determine the values of A and B.

Given

$(2)/(\log (20)-1)=\log _B(A)$

We can rewrite the expression in the denominator using the following rule:

$\log _C(a)-\log _C(b)=\log _C\left((a)/(b)\right)$

Remember that we write log for a logarithm with base 10 and ln for a logarithm with base e, thus we have:

$\log (20)-1=\log (20)-\log (10)=\log \mleft((20)/(10)\mright)=\log (2)$

And rewrite the expression in the numerator using the property:

$\log _C(a^b)=b\cdot\log _C(a)$

Therefore we have:

$2=2\cdot1=2\cdot\log (10)=\log (10^2)=\log (100)$

Finally, we use the following property to find A and B:

$(\log_C(a))/(\log_C(b))=\log _b(a)$

We get that:

$(\log(100))/(\log(2))=\log _2(100)$

And this is equal to:

$\log _2(100)=\log _B(A)$

If only A = 100 and B = 2.

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