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Evaluate the logarithm. 11. log_(4)64underline ( ) 12. log_(3)1underline ( ) 13 7^log_(7x)underline ( )

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Evaluate the logarithm.
11. log_(4)64underline ( )
12. log_(3)1underline ( )
13 7^log_(7x)underline ( )

Evaluate the logarithm. 11. log_(4)64underline ( ) 12. log_(3)1underline ( ) 13 7^log_(7x)underline ( )

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Franciscaélite · Tutor durante 8 años
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11. To evaluate the logarithm $log_{4}64$, we need to find the power to which 4 must be raised to get 64.<br /><br />We can rewrite 64 as $4^3$, since $4^3 = 64$.<br /><br />Therefore, $log_{4}64 = 3$.<br /><br />12. To evaluate the logarithm $log_{3}1$, we need to find the power to which 3 must be raised to get 1.<br /><br />We know that any number raised to the power of 0 is equal to 1.<br /><br />Therefore, $log_{3}1 = 0$.<br /><br />13. To evaluate the expression $7^{log_{7}x}$, we can use the property of logarithms that states $a^{log_{a}b} = b$.<br /><br />In this case, $a = 7$ and $b = x$.<br /><br />Therefore, $7^{log_{7}x} = x$.
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