Question

Which graph shows the solution to the equation below log3x=log0.5x

Answer 1

Graph in attachment.

Explanation:

Graph the equation,
`\log_3x=\log_(0.5)x`

First we make system of equation and then draw the graph of both function.

• First function,
  `y_1=\log_3x`

• Second function,
  `y_2=\log_(0.5)x`

Graph of first function:

Take some random value of x

x : 0.5 1 1.5 2 2.5 3

y₁: -0.6 0 0.4 0.6 0.8 1

y₂: 1 0 -0.6 -1 -1.3 -1.6

Now plot the point of table on same coordinate plane and connect the point by curve line.

Please find the attachment for graph.

Blue line graph for y₂

Red line graph for y₁

Solution of the equation is intersection of the both graph.

Solution: (1,0)