For the logarithmic model y = β 0 + β 1 ln(x)+ ε,the predicted value of y is computed by:

The predicted value of y is given by y = β 0 + β 1 ln(x) + ε. The second term in this equation is β 1 ln(x), which can be rewritten as β 1ln(x^( )). Therefore, the predicted value of y is β 0 + β 1ln(x^( )) + ε. This is equivalent to choice (B).

For the logarithmic model y = β 0 + β 1 ln(x)+ ε,the predicted value of y is computed by:

The predicted value of y is given by y = β 0 + β 1 ln(x) + ε. The second term in this equation is β 1 ln(x), which can be rewritten as β 1ln(x^( )). Therefore, the predicted value of y is β 0 + β 1ln(x^( )) + ε. This is equivalent to choice (B).