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Solve $3_{x}=17$ to two significant digits | ||
---|---|---|

$x$ | $3_{x}$ | Comment |

$2$ | $3_{2}=9$ | $3_{2}<17⇒x>2$ |

$3$ | $3_{3}=27$ | $3_{3}>17⇒x<3$ |

$2.5$ | $3_{2.5}≈15.58845…$ | $3_{2.5}<17⇒x>2.5$ |

$2.6$ | $3_{2.6}≈17.39863…$ | $3_{2.6}>17⇒x<2.6$ |

$2.55$ | $3_{2.55}≈16.46869…$ | $3_{2.55}<17⇒x>2.55$ |

Since the equation's solution is in the interval $2.55<x<2.6,$ an approximate answer with two significant digits is $x≈2.6.$

$y=x_{2}y=4_{x} $

Then, both functions are graphed on the same coordinate plane.
The solution is in the interval $-0.75<x<-0.5.$ To find a better approximation it is necessary to readjust the scale on the $x$-axis and to narrow the interval on which the functions are graphed.

Solver. The screen will then show this.

Next, the left-hand side of the equation should be written on the second line. Then, by pressing the $ENTER $ button, a numerical approximation of the solution is calculated.

To use this particular tool, one side of the equation needs to be equal to $0.$ Therefore, it may be necessary to rearrange the equation before writing it in the calculator.

Numerical methods are helpful when solving complicated equations that cannot be solved algebraically. However, when using numerical methods it is often only possible to find approximations of the solutions. If it is necessary to find an exact solution, algebraic methods in most cases are preferred.