Exercise 78 Page 971

To solve the given logarithmic equation, we will first recall the definition of a logarithm. log_b x=y ⇔ x= b^y This tells us how we can rewrite the logarithm equivalent to y as an exponential equation. The argument x is equal to b raised to the power of y. The base of a natural logarithm is e, so ln x = log_e x. To use this definition, we need to rewrite the given equation.

Now, let's rewrite this equation in exponential form. ln (4x)^2= 3 ⇔ (4x)^2= e^3 We will solve this equation for x. Let's do it!

The exact solutions are x_1= esqrt(e)4 and x_2= - esqrt(e)4. We can also write them in decimal form using a calculator. x_1&=&esqrt(e)/4 &≈ 1.120 x_2&=&- esqrt(e)/4 &≈ - 1.120