document.write( "Question 1005697: Solve the exponential equation using like bases. 64^x-5=256^5x+1 - Show step by step. \n" ); document.write( "
Algebra.Com's Answer #621847 by Boreal(15235)![]() ![]() You can put this solution on YOUR website! 64^x-5=256^5x+1 \n" ); document.write( "64=2^6 \n" ); document.write( "Therefore, 64^x-5=(2^6)^(x-5)=2^(6x-30) by product rule of exponents. \n" ); document.write( "256^(5x+1) \n" ); document.write( "256=2^8 \n" ); document.write( "Therefore, (2^8)^(5x+1)=2^(40x+8) \n" ); document.write( "Set the two equal \n" ); document.write( "40x+8=6x-30. You can do this by taking log 2 of both sides, which removes the base and makes it 1, log 10 10=1 \n" ); document.write( "Solving the above, 34x=-22 \n" ); document.write( "x=-(22/34) or -11/17 \n" ); document.write( "using common denominators in exponents to check \n" ); document.write( "64^(-11-85)/17=64^(-96/17)=6.35 X 10^-11 \n" ); document.write( "256^(-55-17)/17=256^(-72/17)=6.35 x 10^-11\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |