document.write( "Question 823335: I would like help on these questions:\r
\n" ); document.write( "\n" ); document.write( "log base 0.25 of sqrt2 - log base sqrt2 of 0.25\r
\n" ); document.write( "\n" ); document.write( "inverse of y=3*4^(x-1) + 2\r
\n" ); document.write( "\n" ); document.write( "thank you \n" ); document.write( "
Algebra.Com's Answer #495784 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"log%280.25%2C+%28sqrt%282%29%29%29+-+log%28sqrt%282%29%2C+%280.25%29%29\"
\n" ); document.write( "The key to the first problem is to recognize that 0.25 and sqrt(2) are both powers of 2:
\n" ); document.write( "\"0.25+=+1%2F4+=+2%5E-2\"
\n" ); document.write( "\"sqrt%282%29+=+2%5E%281%2F2%29\"
\n" ); document.write( "So by using the change of base formula to change these two logs into expressions of base 2 logs, we will get something that should simplify easily. The change of base formula:
\n" ); document.write( "\"log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29\"
\n" ); document.write( "Using this on both logs we get:
\n" ); document.write( "
\n" ); document.write( "Since we already know what powers of 2 produce 0.25 and sqrt(2), we can replace all the logs:
\n" ); document.write( "\"%281%2F2%29%2F%28-2%29+-+%28-2%29%2F%281%2F2%29\"
\n" ); document.write( "Now we simplify:
\n" ); document.write( "\"%281%2F2%29%281%2F%28-2%29%29+-+%28%28-2%29%2F1%29%282%2F1%29\"
\n" ); document.write( "Multiplying:
\n" ); document.write( "\"%28-1%2F4%29+-+%28-4%29\"
\n" ); document.write( "which simplifies as follows:
\n" ); document.write( "\"%28-1%2F4%29+%2B+4\"
\n" ); document.write( "\"%28-1%2F4%29+%2B+16%2F4\"
\n" ); document.write( "\"15%2F4\"
\n" ); document.write( "\"3%263%2F4\" or 3.75 \n" ); document.write( "
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