1+log3 5=2log2-log3 (x-1)

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To solve the equation 1 + log3 5 = 2log2 - log3 (x-1), we need to simplify both sides of the equation first.

1 + log3 5 = 1 + log3 5

2log2 = log2 4

Now we can rewrite the equation as:

1 + log3 5 = log2 4 - log3 (x-1)

Next, we can use the properties of logarithms to simplify the equation further:

1 + log3 5 = log2 4 - log3 (x-1)
1 + log3 5 = log2 4 - log3 (x-1)
1 + log3 5 = log2 4 - (log3 x - log3 1)

Now we can simplify the equation even further:

1 + log3 5 = log2 4 - log3 x + log3 1
1 + log3 5 = log2 4 - log3 x + 0
1 + log3 5 = log2 4 - log3 x

Now we can solve for x by rearranging the equation:

1 + log3 5 + log3 x = log2 4
log3 5 + log3 x = log2 4 - 1
log3 (5x) = log2 3
5x = 3

Therefore, x = 3/5.