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irina [24]
3 years ago
13

Solve the equation (linear equation)

D%29%5E%7B3x%7D" id="TexFormula1" title="8^{2x+7} = (\frac{1}{32})^{3x}" alt="8^{2x+7} = (\frac{1}{32})^{3x}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Minchanka [31]3 years ago
8 0

Answer: x=-1

Step-by-step explanation:

By the negative exponent rule, you have that:

(\frac{1}{a})^n=a^{-n}

By the exponents properties, you know that:

(m^n)^l=m^{(nl)}

Therefore, you can rewrite the left side of the equation has following:

(\frac{1}{8})^{-(2x+7)}=(\frac{1}{32})^{3x}

 Descompose 32 and 8 into its prime factors:

32=2*2*2*2*2=2^5\\8=2*2*2=2^3

Rewrite:

(\frac{1}{2^3})^{-(2x+7)}=(\frac{1}{2^5})^{3x}

Then:

(\frac{1}{2})^{-3(2x+7)}=(\frac{1}{2})^{5(3x)}

As the base are equal, then:

-3(2x+7)=5(3x)

Solve for x:

-6x-21=15x\\-21=15x+6x\\-21=21x\\x=-1

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