 # Use properties of logarithms to find exactly value. 5^(log_5 6+log_5 7) John Landry 2022-07-27 Answered
Use properties of logarithms to find exactly value.
${5}^{{\mathrm{log}}_{5}6+{\mathrm{log}}_{5}7}$
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Properties to use here:
${A}^{{\mathrm{log}}_{A}\left(x\right)}=x$
$\mathrm{log}\left(a\right)+\mathrm{log}\left(b\right)=\mathrm{log}\left(ab\right)$
${5}^{{\mathrm{log}}_{5}6+{\mathrm{log}}_{5}7}={5}^{{\mathrm{log}}_{5}\left(6\ast 7\right)}={5}^{{\mathrm{log}}_{5}\left(42\right)}=42$
###### Not exactly what you’re looking for? Karsyn Beltran
${5}^{{\mathrm{log}}_{5}6+{\mathrm{log}}_{5}7}$
${5}^{{\mathrm{log}}_{5}42}\left[{\mathrm{log}}_{a}+{\mathrm{log}}_{b}={\mathrm{log}}_{ab}\right]$
$42\left[{a}^{{\mathrm{log}}_{a}x}=x\right]$
42 is the answer.