1) log9x+2log3x=5 9 і 3 основа2) log2(x^2-3)+1=log2(6x-10)

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1) log9x + 2log3x = 5

Rewrite the logarithms using the power rule:

log(9x) + log(3x)^2 = 5

Combine the logarithms using the product and power rules:

log(9x) + log(9x)^2 = 5

Simplify the expression:

log(9x) + log(81x^2) = 5

Combine the logarithms using the product rule:

log(9x * 81x^2) = 5

Simplify the expression:

log(729x^3) = 5

Convert to exponential form:

729x^3 = 10^5

729x^3 = 100000

x^3 = 100000 / 729

x^3 = 137.174

x = ∛137.174

x = 5.600

2) log2(x^2 - 3) + 1 = log2(6x - 10)

Subtract 1 from both sides:

log2(x^2 - 3) = log2(6x - 10) - 1

Use the properties of logarithms to combine the logarithms on the right side:

log2(x^2 - 3) = log2((6x - 10) / 2)

Since the bases are the same, the arguments must be equal:

x^2 - 3 = (6x - 10) / 2

Simplify the equation:

2x^2 - 6 = 6x - 10

Rearrange the equation to set it equal to zero:

2x^2 - 6x + 4 = 0

Solve the quadratic equation by factoring or using the quadratic formula:

(x - 2)(2x - 2) = 0

x = 2 or x = 1

Therefore, the solutions to the equation are x = 2 or x = 1.