Question 85348
Given:
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{{{4^(x+6) = 7}}}
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Solve for x
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Take the log base 10 of both sides and you get:
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{{{log((4^(x+6))) = log((7))}}}
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One of the rules of logarithms is that if you have the logarithm of a quantity that is
raised to an exponent, it is equivalent to the exponent times the logarithm of just the
quantity.
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In this problem that translates to multiplying the exponent of (x + 6) times the logarithm of 4.
This makes the equation become:
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{{{(x+6)*log((4)) = log((7))}}}
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Divide both sides of the equation by log(4). When you do, the resulting equation is:
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{{{(x+6) = (log((7))/log((4)))}}}
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Next subtract 6 from both sides of the equation to get:
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{{{x = -6 + (log((7))/log((4)))}}}
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This is the basic answer. You can convert this to decimals by using a calculator  to determine
the values of log(7) and log(4). When you do that you get that log(7) = 0.84509804 and
log(4) = 0.602059991. Substituting these results in:
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{{{x = - 6 +(0.84509804/0.602059991)}}}
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The division results in the equation becoming:
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{{{ x = -6 + 1.403677461 = -4.596322539}}}
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Hope this helps you understand the problem and how to use logarithms to solve it.