<h2>Power law</h2>
<code>logbpn = n * logbp</code>
Proof:
<code>logbp = a</code> -> <code>ba = p</code>
Raise to <code>k</code> -> <code>bk*a = pk</code>
Apply <code>logb</code> -> <code>k * a = logbpk</code>
Replace <code>a</code> with <code>logbp</code> -> <code>k * logbp = logbpk</code>
<h2>Product law</h2>
<code>logbm*n = logbm + logbn</code>
Proof:
<code>logbm = i</code> -> <code>bi = m</code> &#x26; <code>logbn = j</code> -> <code>bj = n</code>
Multiply -> <code>bi * bj = m * n</code>
Simplify -> <code>bi+j = m * n</code>
Apply <code>logb</code> -> <code>i + j = logbm*n</code>
Replace <code>i</code> and <code>j</code> -> <code>logbm + logbn = logbm*n</code>
<h2>Quotient law</h2>
<code>logbm/n = logbm - logbn</code>
Proof:
<code>logbm = i</code> -> <code>bi = m</code> &#x26; <code>logbn = j</code> -> <code>bj = n</code>
Divide -> <code>bi / bj = m / n</code>
Simplify -> <code>bi-j = m / n</code>
Apply <code>logb</code> -> <code>i - j = logbm/n</code>
Replace <code>i</code> and <code>j</code> -> <code>logbm - logbn = logbm/n</code>

A quick recap of some fundamental properties of logarithms

MicroPosts

Power law

Product law

Quotient law

PinkLetter

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