# SOLUTION: Solve for x log10 (5-x) = 3 log10 2

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 Question 119247: Solve for x log10 (5-x) = 3 log10 2Found 2 solutions by stanbon, bucky:Answer by stanbon(57290)   (Show Source): You can put this solution on YOUR website!log10 (5-x) = 3 log10 2 log10 (5-x) = log10 2^3 Take the anti-log of both sides to get: 5-x = 8 x = -3 =============== Cheers, Stan H. Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!Given: . . On the right side you can take the multiplier 3 to the inside of the log operator if you make it an exponent. This makes the equation become: . . Continuing on the right side, cube the 2 to get 8, making the equation become: . . Notice that both sides have an operator of log to the base 10. For both sides of this equation to be equal, the quantities that the log operator is applied to must be equal. This means that . 5 - x must equal 8. In equation form this is: . 5 - x = 8 . Get rid of the 5 on the left side by subtracting 5 from both sides to get: . -x = 3 . Solve for x by multiplying both sides of this equation by -1 and the result is: . x = -3 . That's the answer. You can check it by substituting -3 for x in the original equation you were given. Start with the original equation of: . . Substitute -3 for x and this equation becomes: . . Simplify the left side by recognizing that 5 - (-3) = 5 + 3 = 8. This makes the equation become: . . Using a calculator you can determine that the base 10 log of 8 is 0.903089987 and the base 10 log of 2 is 0.301029995. Substituting these values results in: . . If you multiply out the right side you will see that this equation is true, and therefore the answer of x = -3 is correct. . Hope this helps you to work your way through this problem. .