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2025 AMC 12A Problems/Problem 7: Difference between revisions

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<imath>log</imath> <imath>k</imath> * <imath>5^am^b</imath> <imath>=</imath> <imath>4+2logm</imath>. We can now use logarithmic properties to rewrite this as:
<imath>log</imath> <imath>k</imath> * <imath>5^am^b</imath> <imath>=</imath> <imath>4+2logm</imath>. We can now use logarithmic properties to rewrite this as:
<cmath>log</cmath> <imath>k</imath> * <imath>5^am^b</imath> <imath>=</imath> <imath>log10^4*m^2</imath>
<imath>log</imath> <imath>k</imath> * <imath>5^am^b</imath> <imath>=</imath> <imath>log10^4*m^2</imath>

Revision as of 16:39, 6 November 2025

Solution 1: Taking the logarithm of both sides and using n = 5, we have:

$log$ $k$ * $5^am^b$ $=$ $4+2logm$. We can now use logarithmic properties to rewrite this as: $log$ $k$ * $5^am^b$ $=$ $log10^4*m^2$

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