So this is question.
2^x .2^y=3^z

simplify the LHS of equation by the combining factors which have same bases.

2^(x+y)=3^z

Take log to both sides of equation,

log{2^(x+y)}= log {3^z}

by property of logs,

x+y(log2) =z( log 3)

where log3 =0.4771
and log 2= 0.3010

Put in the above equation,we get


x+y(0.3010) = z(0.4771)

divide the equation by z,and divide by 0.3010 both sides we get,

(x+y)/ z = 0.4771/ 0.3010 => 1.5859

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