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Logarithmic Equations Solver - Find the Solution Easily

Solve logarithmic equations instantly with this helpful tool. Just enter the equation and get the answer right away.

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Logarithmic Equations Solver - Find the Solution Easily

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  1. x log 4 = log 11 4 4 Takelogof each side. 4 x = log 11 x = 11 log 4 x 4 = 11 log 4 x x Solve 4 = 11. log b = x b The solution is about 1.73. Check this in the original equation. ANSWER x 1.73 EXAMPLE 2 Take a logarithm of each side SOLUTION Write original equation. Change-of-base formula Use a calculator.

  2. EXAMPLE 3 Use an exponential model Cars You are driving on a hot day when your car overheats and stops running. It overheats at 280°F and can be driven again at 230°F. If r = 0.0048 and it is 80°F outside,how long (in minutes) do you have to wait until you can continue driving?

  3. Substitute for T, T , T, and r. R ° x x 230 = (280 – 80)e + 80 Ine = log e = x –0.0048t –0.2877 –0.0048t e –0.0048t 0.75 =e –0.0048t 150 = 200e –0.0048t ln 0.75 = ln e 60 t –rt T = ( T – T )e + T R ° R EXAMPLE 3 Use an exponential model SOLUTION Newton’s law of cooling Subtract 80 from each side. Divide each side by 200. Take natural log of each side. Divide each side by –0.0048.

  4. ANSWER You have to wait about 60 minutes until you can continue driving. EXAMPLE 3 Use an exponential model

  5. 9x 5. 7 = 15 x 4. 2 = 5 –0.3x 6. 4e –7 = 13 for Examples 2 and 3 GUIDED PRACTICE Solve the equation. SOLUTION about 2.32 about 0.155 SOLUTION SOLUTION about–5.365

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