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Chapter 5: Q. 15 (page 351)

Solve each equation.

log ( x + 9 ) = 2

Short Answer

Expert verified

The value of x is 91.

Step by step solution

01

Step 1. Given Information

Given equationlog ( x + 9 ) = 2

We have to solve the equation for the value of x.

02

Step 2. Solution

Logarithmic function is good defined only if the argument of logarithmic function is a positive real number (logbx,x>0)

Therefore, the solutions of equation log(x+9)=2must be

x+9>0鈬�x>-9---(1)

Using a formula

y=logax鈬�x=aya>0,a鈮�1(wherea=10andy=2)weget:log(x+9)=2x+9=102x+9=100x=91

The solution is greater than -9 (because of (1)), so the solution of the given equation is x = 91

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