# math

posted by .

Hello,

Is log_3 (5) equal to log_5 (3)? Explain your answer. Do not evaluate the logarithms.

is my question. What is a surefire way to show this is false.

• math -

let x = log (base3) 5
then 3^x = 5 , clearly x > 1 ,
because 3^1 = 3 and 3^2 = 25 ,so x must be between 1 and 2

let y = log(base5)^3
then 5^y = 3 , clearly y < 1,
because 5^0 = 1 and 5^1 = 5
so y has to be between 0 and 1
so x ≠ y
and the two log expressions cannot be equal

• math -

fantastic, makes so much sense now, thx

• math -

and btw 3^2 = 25 is typo

## Similar Questions

1. ### Math - Logarithmic

log_5[log_4(log_3(x))] = 1 log_5 = log with the base of 5 log_4 = log with the base of 4 log_3 = log with the base of 3 Answer: 3^1024 Too many logs in one equation. . .I don't know how to solve it
2. ### Math - Logarithmic

Solve: 2log_3(x) - log_3(x-2) = 2 My Work: log_3(x^2) - log_3(x-2) = log_3(3^2) log_3 [(x^2) / (x-2)] = log_3(27) (x^2) / (x-2) = 27 x^2 = (x-2)(27) x^2 = 27x - 54 x^2 - 27x = -54 27x = -54 x = -2 Textbook Answer: 3 or 6 Where did …
3. ### Math - logs

log_3(2x - 1) = 2, Find x. Here's what I've done: log_3(2x) * log_3(1) = 2 log2x/log3 * log1/log3 = 2 trial and error... log2 (2*1.4)/log3 * 0 = 2.03... x = 1.4 I think I did it wrong because anything that multiplies with 0 gives you …
4. ### ICA Honors

1/log_2(X) + 1/log_3(x) + 1/log_4(x) +1/log_5(x) =log_5(625)
5. ### Math: Homework Questons (answer quick)

Can you check if the answer is correct and of there any grammar mistakes. Write True or False and EXPLAIN your reasoning for the answer!!!! 8. (5 - 2) - 1 = 5 - (2 - 1) Answer: True Reason: The reason why my answer to this question …
6. ### precalculus

solve logarithmic equation in exact form only. show work. log_5(x-3)+ log_5(x-6)-log_5(x+1)=2
7. ### math

Is log_3 (5) equal to log_5 (3)? Explain your answer. Do not evaluate the logarithms.
8. ### math

find derivative of f(x)= log_5((x-4)^3) + e^((x-1)(x+1)) Log_5 means log base 5
9. ### algebra

Need some one check my homework. Evaluate 3p/q when p=2 and q=6. Answer:1 Use < > or = for __ to write a true sentence: 0.001 __ 0.0010 Answer:< Question 3 Evaluate -3/8 - 5/8. Answer:7 Question 4 Evaluate: 84 + (-99) + 44 …
10. ### Trigonometry (Logarithmic Function)

If log_5(9) = 1.365 and log_5(2)=0.431, then what is log_5(24)?

More Similar Questions