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Chapter 8: Q. 13 (page 556)

Solve log3x+8+log3x=2.

Short Answer

Expert verified

The value ofxis 1.

Step by step solution

01

Step 1. given Information

The given equation islog3x+8+log3x=2.

02

Step 2. Use Logarithmic Properties

  • Use the property logax+logay=loga(xy)and simplify the equation.

log3x+8x=2

  • Now, use the property, logax=y鈬�x=ayto rewrite the equation.

xx+8=32xx+8=9

03

Step 3. Solve the Quadratic Equation

  • The obtained equation can be simplified to x2+8x-9=0.
  • Factor the equation and find its roots.

x2+9x-x-9=0x+9x-1=0x=1,-9

  • The logarithmic functions are not defined on negative integers.
  • So,x=1.

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