3^x=x^5 what numbers make this true please give answers to the 2nd decimal
3^x = x ^5 take the log of both sides
log 3^x = logx^5 and we can write
x log3 = 5 log x
Rearrange
x / log x = 5/log 3
Mmmm....that doesn't look too promising, does it???
Let's just graph the original functions and see where they meet (if they do....!!)
Here's a partial graph......https://www.desmos.com/calculator/roelalpkth
The graph shows that one solution occurs at about (1.343, 4.375)
Another solution occurs at about (10.351, 150,462).....shown here....https://www.desmos.com/calculator/ujgxybuyeq
This happens because from x values (-∞, 1.343), the graph of 3^x > x^5. Then from (1.343, 10.351), the graph of x^5 > 3^x. Finally, the graph of 3^x "overtakes" the graph of x^5 at about x = 10.351, and is always greater at any comparavle x value after that - as we would expect....!!!!
3^x = x ^5 take the log of both sides
log 3^x = logx^5 and we can write
x log3 = 5 log x
Rearrange
x / log x = 5/log 3
Mmmm....that doesn't look too promising, does it???
Let's just graph the original functions and see where they meet (if they do....!!)
Here's a partial graph......https://www.desmos.com/calculator/roelalpkth
The graph shows that one solution occurs at about (1.343, 4.375)
Another solution occurs at about (10.351, 150,462).....shown here....https://www.desmos.com/calculator/ujgxybuyeq
This happens because from x values (-∞, 1.343), the graph of 3^x > x^5. Then from (1.343, 10.351), the graph of x^5 > 3^x. Finally, the graph of 3^x "overtakes" the graph of x^5 at about x = 10.351, and is always greater at any comparavle x value after that - as we would expect....!!!!