solve-log-7-2-log-49-x-log-7-3-

Question Number 171990 by Mikenice last updated on 22/Jun/22

s o l v e :

{l o g}_{7} 2 + {l o g}_{49} x = {l o g}_{7} \sqrt{3}

Answered by nurtani last updated on 23/Jun/22

\Leftrightarrow {l o g}_{7} 2 + {l o g}_{7} x^{\frac{1}{2}} = {l o g}_{7} 3^{\frac{1}{2}}

\Leftrightarrow {l o g}_{7} 2 x^{\frac{1}{2}} = {l o g}_{7} 3^{\frac{1}{2}}

\Leftrightarrow 2 x^{\frac{1}{2}} = 3^{\frac{1}{2}}

\Leftrightarrow {(2 x^{\frac{1}{2}})}^{2} = {(3^{\frac{1}{2}})}^{2}

\Leftrightarrow 4 x = 3

\Leftrightarrow x = \frac{3}{4}

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