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logy x=3 logy (4x)=5

Guest Sep 25, 2014

Best Answer 

 #1
avatar+19480 
+5

logy x=3 logy (4x)=5

$$\small{\text{
$
\begin{array}{rclc|rclc}
\log_y{ (x) } & = & 3 & | \quad y^{()} \quad & \quad \log_y {(4x)} & = & 5 \quad | \quad y^{()} \\
y^{\log_y{ (x) }} & = & y^3 & \quad & \quad y^{\log_y {(4x)}} & = &y^5 \\
x & = & y^3 & \quad & \quad 4x & = & y^5 \\
& & & & 4y^3 & = & y^5 \quad | \quad :y^3 \\
& & & & 4 & = & y^2 \quad | \quad \sqrt \\
& & & & 2 & = & y \\
x & = & 2^3 & & y & = & 2 \\
x & = & 8 & & y & = & 2 \\
\end{array}
$
}}$$

$$\small{\text{
$ \log_2{(8)}=3 \qquad \log_2{(4*8)}=5
$
}}$$

heureka  Sep 26, 2014
 #1
avatar+19480 
+5
Best Answer

logy x=3 logy (4x)=5

$$\small{\text{
$
\begin{array}{rclc|rclc}
\log_y{ (x) } & = & 3 & | \quad y^{()} \quad & \quad \log_y {(4x)} & = & 5 \quad | \quad y^{()} \\
y^{\log_y{ (x) }} & = & y^3 & \quad & \quad y^{\log_y {(4x)}} & = &y^5 \\
x & = & y^3 & \quad & \quad 4x & = & y^5 \\
& & & & 4y^3 & = & y^5 \quad | \quad :y^3 \\
& & & & 4 & = & y^2 \quad | \quad \sqrt \\
& & & & 2 & = & y \\
x & = & 2^3 & & y & = & 2 \\
x & = & 8 & & y & = & 2 \\
\end{array}
$
}}$$

$$\small{\text{
$ \log_2{(8)}=3 \qquad \log_2{(4*8)}=5
$
}}$$

heureka  Sep 26, 2014
 #2
avatar+92623 
+3

Nice one Heureka,     

I didn't even realise that I was being presented with 2 equations to solve simultaneously!  

I didn't understand WHAT the question was.  Perhaps you could present it a little better next time anonymous.

Heureka may not be around to interprete!   

Anyway, that is a really nice solution Heureka.  

Melody  Sep 26, 2014

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