document.write( "Question 238003: 4.6^x-76=0 \n" ); document.write( "

Algebra.Com's Answer #174929 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
With the variable in the exponent like in this problem, start by getting the equation into one of the following forms:
\n" ); document.write( "base^(expression-with-variable) = other-expression
\n" ); document.write( "or
\n" ); document.write( "base^(expression-with-variable) = base^(other-expression)

\n" ); document.write( "Since your equation only has one term with an exponent (that is not one), we will use the first form. Adding 76 to both sides gets us to the desired form in one step:
\n" ); document.write( " $\"4.6%5Ex+=+76\"$
\n" ); document.write( "Now that we have the equation in the desired form, we find the logarithm of both sides. The base of the logarithm should be one your calculator can handle. Most calculators, if they can do any logarithms, can handle base 10 logarithms so that is what I will use here. (Some calculators also do base e (or natural) logarithms which can used if you want. The answer will work out the same regardless of the base of the logarithm used.)
\n" ); document.write( " $\"log%28%284.6%5Ex%29%29+=+log%28%2876%29%29\"$
\n" ); document.write( "Now we can use a property of logarithms to \"extract\" x from the exponent: $\"log%28a%2C+%28x%5Ey%29%29+=+y%2Alog%28a%2C+%28x%29%29\"$ . (This is the reason we are using logarithms. Somehow we had to get x out of the exponent.)
\n" ); document.write( " $\"x%2Alog%28%284.6%29%29+=+log%28%2876%29%29\"$
\n" ); document.write( "Now that x is out of the exponent, we can solve for it. We just divide both sides by log(4.6):
\n" ); document.write( " $\"x+=+log%28%2876%29%29%2Flog%28%284.6%29%29\"$
\n" ); document.write( "Now just use your calculator to find x. Find the two logarithms and then divide. (Be sure to do it in that order. You will get the wrong answer if you divide 76 by 4.6 and then find the logarithm.) \n" ); document.write( "

\n" );