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# algebra 113

### common and natural logarithms, change of base, equations and applications

Question | Answer |
---|---|

Find exact value of 1n 8 exponent square root e | e exponent x means loge(little e) exponent x=x answer; 1n e1/8=12/8 |

Solve the equation for x-give an exact solution and a 4-decimal-place approximation logx=3.1 | Find exact solution, write the equation in exponential notation such that it can be evulated with a calculator. 10exponent 3.1=x, 10 exponent 3.1 is the exact solution. |

Find the exact value log 1 over 100,000 | common logarithms logx means log 10 exponent x. Remember log 10 exponent x meand log (little 10) 10 exponent x=x. Answer; log 10 exponent-5=-5 |

Solve the equation for x. Give an exact solution and a 4-decimal-place approximation logx=3.1 | The exact solution is 10 exponent 3.1. 10 exponent 3.1 approximated to 4 decimal places is 1258.9254 |

Solve the equation. Give an exact solution and also approximate the solution to 4 decimal places. 11(x+7)(exponents)=2 | a exponent x=a exponent y to x=y Take the logarithm of each side. log 11 exponents x+7=log2. Use properties of logarithms. Solve for x and calculate the value of x. Solution is log2 over log 11 -7 or approximately -6.7109 |

Solve the equation log15(x to the second power-14x)=1 | Notice that x exponent 2-14x must be positive with this in mind, write an equivalent exponential equation using the definition of logarithms. log a b=y is equivalent to a exponent 4=b |

Created by:
Pferman