To solve these logarithmic equations, we need to rewrite the equations in exponential form first.
1) (Lg(x-0.09)+log_{0.01}(9)=0)
The equation in exponential form is:(\lg(x-0.09) \times 0.01^{log_{0.01}(9)} = 1)
Now, let's simplify the equation:(\lg(x-0.09) \times 0.01^{log_{0.01}(9)} = 1) becomes (\lg(x-0.09) \times 9 = 1)
Now, we can rewrite the equation in exponential form:[10^9 = x-0.09]
Solving for x:[x = 10^9 + 0.09]
Therefore, the value of x is approximately 1000000000.09.
2) (Log_{0.25}(6x-5)=-2)
The equation in exponential form is:(0.25^{-2} = 6x-5)
Simplify the equation:(4 = 6x-5)
Now, we can rewrite the equation in exponential form:[6x = 9]
Solving for x:[x = \frac{9}{6}]
Therefore, the value of x is 1.5.
To solve these logarithmic equations, we need to rewrite the equations in exponential form first.
1) (Lg(x-0.09)+log_{0.01}(9)=0)
The equation in exponential form is:
(\lg(x-0.09) \times 0.01^{log_{0.01}(9)} = 1)
Now, let's simplify the equation:
(\lg(x-0.09) \times 0.01^{log_{0.01}(9)} = 1) becomes (\lg(x-0.09) \times 9 = 1)
Now, we can rewrite the equation in exponential form:
[10^9 = x-0.09]
Solving for x:
[x = 10^9 + 0.09]
Therefore, the value of x is approximately 1000000000.09.
2) (Log_{0.25}(6x-5)=-2)
The equation in exponential form is:
(0.25^{-2} = 6x-5)
Simplify the equation:
(4 = 6x-5)
Now, we can rewrite the equation in exponential form:
[6x = 9]
Solving for x:
[x = \frac{9}{6}]
Therefore, the value of x is 1.5.