Math

QuestionSolve for xx in the equation 74×7x711=1\frac{7^{4} \times 7^{x}}{7^{11}}=1. Find x=x=

Studdy Solution

STEP 1

Assumptions1. The base of the exponent is7. The exponent law am×anap=am+np\frac{a^{m} \times a^{n}}{a^{p}} = a^{m+n-p} is applicable3. The equation is 74×7x711=1\frac{7^{4} \times7^{x}}{7^{11}}=1

STEP 2

We can simplify the left side of the equation using the exponent law am×anap=am+np\frac{a^{m} \times a^{n}}{a^{p}} = a^{m+n-p}.
74×7x711=74+x11\frac{7^{4} \times7^{x}}{7^{11}} =7^{4+x-11}

STEP 3

implify the exponent.
7+x11=7x77^{+x-11} =7^{x-7}

STEP 4

Since 7x7=17^{x-7}=1, we know that any number (except0) to the power of0 is1. Therefore, x7=0x-7=0.

STEP 5

olve for x.
x7=0x-7=0x=7x=7So, x=7x=7.

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