solve the logarithmic equation. Remember to check for extraneous solutions:

Question

show step by step work:

17^22x-3=11^2x+9

Answer 1

Move the terms

22x-3=2log base 17 (11)x + 9log base 17 (11)

Factor the expression

22x - 2log base 17 (11)x + 9log base 17 (11) + 3

Divide both sides

22 - 2log base 17 (11)x + 9log base 17 (11) + 3

Rewrite convert

x= 9log base 17 (11) + 3 /22 - 2log base 17 (11)

Simplify the expressions

x=log17(11^9 * 17^3) + log17(17^3)/log17(17^22)+log17(11^ -2)

Express with a positive exponent

x= log17(11^9 * 17^3)/log17(17^22 * 11^ -2)

Evaluate

x=log17(11^9 * 17^3)/log17(17^22 * 1/11^2)

Calculate

x=log17(11^9 * 17^3)/log17(17^22 * 1/121)

Simplify the expression

x=log17(11^9 * 17^3)/log17(17^22/121)

Write in exponential form

x=log base 17^22/121(11^9 * 17^3)

Transform the expression

x=log(17^11/11)^2 (11^9 * 17^3)

Evaluate

x= 1/2 * log(17^11/11) (11^9 * 17^3)

Reorder the terms

x=1/2 * log 17^11/11 (11^9 * 4913)

Solution

x= 1/2 * log 17^11/11 (4913 * 11^9)

x= 0.52282520