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Angelina_Jolie [31]
3 years ago
15

What is the solution set for x in log4(x+5)+log4x=log4 14

Mathematics
1 answer:
marishachu [46]3 years ago
3 0
log_ {4} (x+5) + log_4(x) = log_4(14)

For logs with same base :

log_b(f(x)) + log_b(g(x)) = log_b(f(x)*g(x))

Log_4(x+5) + log_4(x) =log_4((x+5)x)

log_4((x+5) = log_4(14)

When the logs have the same base :

log_b(f(x)) = log_b(g(x))

F(x) = g(x)

For log_4((x+5)x) = log_4(14)

Solve (x+5)x = 14

expand

(x+5)x = x^2 + 5x

x^2+5x+14

(x-2)(x+7) = 0

x = 2 , x = - 7

Therefore, the final solution : x = 2

hope this helps!





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