To solve this logarithmic equation, we will start by using the property of logarithms that states loga(b) = c is equivalent to a^c = b.
Given:log7(9x+5) = 1/2 log7√10
Apply the property loga(b) = c: a^c = b
7^(log7(9x+5)) = 7^(1/2 log7√10)
9x + 5 = √10^(1/2)
9x + 5 = √10
9x = √10 - 5
x = (√10 - 5)/9
Therefore, x = (√10 - 5)/9 is the solution to the equation.
To solve this logarithmic equation, we will start by using the property of logarithms that states loga(b) = c is equivalent to a^c = b.
Given:
log7(9x+5) = 1/2 log7√10
Apply the property loga(b) = c: a^c = b
7^(log7(9x+5)) = 7^(1/2 log7√10)
9x + 5 = √10^(1/2)
9x + 5 = √10
9x = √10 - 5
x = (√10 - 5)/9
Therefore, x = (√10 - 5)/9 is the solution to the equation.