If 3^x = 4^x-1, then x=
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Let us write the equations again.
3^x = 4^x-1
3^x = 4^x / 4
of 4 * 3^x = 4^x
To solve this, let us take log on both sides. Taking log on both sides, we get
log 4 + x log 3 = x log 4
or x (log4-log3) = log 4
or x = log 4 / (log 4 - log 3)
log 4 = 0.6021 and log 3 = 0.4771
Thus, we get x = 0.6021 / (0.6021-0.4771) = 0.6021/0.125 = 4.8168
Thus, x = 4.8168.
To check, let us find the values of 3^4.8126 and 4^(4.8168-1)
3^4.8168 = 198.6999, or 198.7
4^(4.8168-1) = 4^3.8168 = 198.5832 or 198.6
Since we had taken the logs on both sides, there is a slight error in the values, otherwise, the values are quite close.
Thus, x = 4.8168.
3^x = 4^x-1
3^x = 4^x / 4
of 4 * 3^x = 4^x
To solve this, let us take log on both sides. Taking log on both sides, we get
log 4 + x log 3 = x log 4
or x (log4-log3) = log 4
or x = log 4 / (log 4 - log 3)
log 4 = 0.6021 and log 3 = 0.4771
Thus, we get x = 0.6021 / (0.6021-0.4771) = 0.6021/0.125 = 4.8168
Thus, x = 4.8168.
To check, let us find the values of 3^4.8126 and 4^(4.8168-1)
3^4.8168 = 198.6999, or 198.7
4^(4.8168-1) = 4^3.8168 = 198.5832 or 198.6
Since we had taken the logs on both sides, there is a slight error in the values, otherwise, the values are quite close.
Thus, x = 4.8168.
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