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Varvara68 [4.7K]
3 years ago
10

Solve for the following equation step by step and justify your steps when using an exponential property.

Mathematics
1 answer:
mel-nik [20]3 years ago
4 0

x = \frac{5}{7}

using the ' laws of exponents '

• a^{m} × a^{n} = a^{( m + n )}

•  a^{m} ÷ a^{n} = a^{(m - n)}

• (a^{m})^n = a^{mn}

7^{2} × 7^{3} = 7^{5} ÷ 7^{3x} = 7^{5 - 3x}

7^{4x} = 7^{5 - 3x}

equating the exponents since bases on both sides are 7

4x = 5 - 3x

7x = 5 ⇒ x =\frac{5}{7}




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