Question

find the value of x if 5 upon 7 raise to the power 6 and 7 upon 5 raise to the power minus 9 is equal to 5 upon 7 power 3x​

Answer 1

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Answer 2

The value of x is 5

• Given,

               $(\frac{5}{7} )^{6} (\frac{7}{5} )^{-9} = (\frac{5}{7})^{3x}$ ----------------(1)

• We know that,

               $a^{-m} = \frac{1}{a^{m} }$

             $(\frac{7}{5})^{-9} = \frac{1}{(\frac{7}{5})^{9} } = (\frac{5}{7} )^{9}$

• Substituting above value in (1), it becomes

              $(\frac{5}{7})^{6} (\frac{5}{7})^{9} = (\frac{5}{7})^{3x}$ -------------------(2)

• Bases are same, powers must be added

               $a^{m} a^{n} = a^{m+n}$

• Applying above rule in (2), we get

               $(\frac{5}{7} )^{6+9} = (\frac{5}{7} )^{3x} \\(\frac{5}{7} )^{15} = (\frac{5}{7} )^{3x}$

• Bases are same in equation, powers must be equated

                $a^{m} = a^{n}$  ⇒ $m = n$

• Using above rule, we get

                   15 = 3x

                    x = $\frac{15}{3}$ = 5