SECTION 10.6 Exponential and Logarithmic Equations; Further Applications 619
Recall that the x-intercepts of the graph of a function fcorrespond to the real
solutions of the equation In Example 1,we solved the equation
algebraically using rules for logarithms and found the solution set to be
This can be supported graphically by showing that the x-intercept of the graph of the
function defined by corresponds to this solution. SeeFIGURE 17.
For Discussion or Writing
In Example 5,we solved to find the solution set
(We rejected the proposed solution since it led to the logarithm of a negative
number.) Show that the x-intercept of the graph of the function defined by
y=log x+log 1 x- 212 - 2 supports this result.
- 4
log x+ log 1 x- 212 = 2 5256.
y= 3 x- 12
5 2.262 6.
ƒ 1 x 2 =0. 3 x = 12
CONNECTIONS
10–15–2 5FIGURE 17Complete solution available
on the Video Resources on DVD
10.6 EXERCISES
Many of the problems in these exercises require a scientific calculator.Solve each equation. Give solutions to three decimal places. See Example 1.Solve each equation. Use natural logarithms. When appropriate, give solutions to three deci-
mal places. See Example 2.25.Solve one of the equations in Exercises 13–16using common logarithms rather than nat-
ural logarithms. (You should get the same solution.) Explain why using natural logarithms
is a better choice.
26.Concept Check If you were asked to solvewould natural or common logarithms be a better choice? Why?10 0.0025x=75,ln e^2 x=p eln 2x=eln^1 x+^12 eln^16 - x^2 =eln^14 +^2 x^2ln e0.45x= 27 ln e0.04x= 23 ln e-x=pe-0.103x= 7 ln e^3 x= 9 ln e^2 x= 4e0.012x= 23 e0.006x= 30 e-0.205x= 94 x-^2 = 53 x+^242 x+^3 = 6 x-^132 x+^1 = 5 x-^12 x+^3 = 5 x 6 x+^3 = 4 x 2 x+^3 = 3 x-^46 - x+^1 = 22 32 x= 14 5 0.3x= 117 x= 5 4 x= 3 9 - x+^2 = 13