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

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: $log$ $k$ * $5^am^b$ $=$ $log10^4*m^2$

@@ Line 2: / Line 2: @@
 Taking the logarithm of both sides and using n = 5, we have:
-<imath>log</imath> <imath>k</imath> * <imath>5^am^b</imath> <imath>=</imath> <imath>4+2logm</imath>, which we can rewrite 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:
-<imath>log</imath> <imath>k</imath> * <imath>5^am^b</imath> <imath>=</imath> <imath>log10^4*m^2</imath>
+<cmath>log</cmath> <imath>k</imath> * <imath>5^am^b</imath> <imath>=</imath> <imath>log10^4*m^2</imath>