Exponents: solve for the variable

*Solving exponential equations of the same base.*

Step 1. |
Ignore the bases, and simply set the exponents equal each other |

Step 2. |
Solve for the variable |

*Solve for x*
*4*^{x}=4^{9} x=9

*Solve for x*
*4*^{x+1}=4^{9} x+1=9

x=9-1

x=8

*Solving exponential equations of with unlike bases.*

Step 1. |
Rewrite the bases as powers of a common base |

Step 2. |
Substitute the rewritten bases into original equation |

Step 3. |
Simplify exponents |

Step 4. |
Solve like an exponential equation of like bases |

*Solve for x*
*4*^{3}=2^{x} (2^{2})^{3}=2^{x}

2^{6}=2^{x}

6=x

x=6