Question #611c6

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Answer 1 · 2017-05-27T17:03:31

The answer is $-1.1832$ .

Follow the image, please.

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Answer 2 · 2017-05-27T17:06:22

Given: $7^(x+2) + 7^x=5$

Use the property that says addition of exponents is the same as multiplication of the base to each respective exponent:

$7^2 7^x + 7^x=5$

There is a common factor of $7^x$ that can be moved outside parentheses:

$(7^2 + 1)7^x=5$

Square 7:

$(49 + 1)7^x=5$

$(50)7^x=5$

Divide both sides by 50:

$7^x=5/50$

$7^x=1/10$

Use the base 10 logarithm on both sides:

$log_10(7^x)=log_10(1/10) = -1$

Use the property that brings the exponent outside of a logarithm:

$xlog_10(7)=-1$

$x = -1/log_10(7)$